% serremodpq.tex \documentclass{article} \title{Serre's Conjecture Mod $pq$?} \author{B. Mazur\and W.A. Stein} \date{January 11, 1999} \newcommand{\comment}[1]{} \begin{document} \maketitle \tableofcontents \section{Introduction} I haven't yet written an introduction, but here are some helpful remarks as to how to read the table. Please see Barry Mazur's letter below which motivated the computation. Basically, when both an $f$ and $g$ occur together in a given row, then ``Serre's Conjecture mod $pq$'' for a certain representation has an easy positive answer. The rows of the congruence table contain an $f$ whenever the corresponding eigenform at level $NM$ is congruent to the reduction of $f$ modulo the prime $P$ listed in the first column, at least to the precision computed. Similarly for $g$. In some cases the program did not perform a complete check that the forms were congruent to the precision computed, but only checked, with {\em high} probability, that there is a congruence to that precision. In such cases this is indicated by a question mark subscript. In many cases Ribet's theorem implies that there must be a congruence. I do not know if Sturm's result can be applied in this context because the congruence is only checked for those $a_p$ for which $p$ is prime to $NMpq$. In a few cases it was too much extra work to reduce the prime level $\leq 97$ eigenforms modulo $2$, and so this is not done, even though $2$ might be among the canidate pairs $(P, Q)$. This is indicated above the relevant table. The eigenforms refered to in the congruence table are uniquely determined, up to conjugacy, by a factor of the characteristic polynomial of some Hecke operator. These factors are given, so that further investigation of particular eigenforms is possible. To understand why this table was computed, see the letter from Barry Mazur in the last section. Note that the congruence table does {\em not} omit primes for which the corresponding representations are reducible. \section{Letters} \newcommand{\Q}{\mathbf{Q}} \newcommand{\GL}{{\rm GL}} \newcommand{\Z}{\mathbf{Z}} \newcommand{\mod}{{\rm\,\, mod\,\,}} \begin{verbatim} From: Barry Mazur Subject: SERRE'S CONJECTURE MOD PQ To: William Stein \end{verbatim} Dear William, To put perspective on the subject of this e-mail, let me begin with an utterly untestable version of what I was suggesting to you. Let $p$ and $q$ be distinct prime numbers and $G$ the Galois group of the maximal algebraic extension of $\Q$ unramified outside a finite set $S$ of primes. Suppose that we have an odd continuous representation $r: G \rightarrow \GL_2(\Z/pq\Z)$ which is irreducible when reduced mod $p$ and mod $q$. Is $r$ "modular"? To begin to give {\em some} shape to the above question, we might as well assume the ``classical'' Serre conjecture for single primes, so we can start out by giving ourselves two modular newforms $f$ and $g$ and then look for a modular newform $h$ that is congruent mod $p$ to $f$ and mod $q$ to $g$ -- under the assumption that the associated Galois representations mod $p$ and mod $q$ respectively are irreducible. I should be more careful about what I mean ``mod $p$'' and ``mod $q$'': I really mean to take $p$ and $q$ prime ideals in the ring generated by the Fourier coefficients of $f$ and $g$, and ditto with regard to $h$. To simplify one's life, one can "start out" by working only with pairs $f$ and $g$ of newforms whose ring of Fourier coefficients is $\Z$ (i.e., the $f$ and $g$ in question correspond to elliptic curves). But even if one does this, one has to face the possibility (the ``probability'', in fact) that $h$, if it exists at all, no longer has its ring of Fourier coefficients equal to $\Z$. Of course, phrased this way, our qeustion is still relatively un``falsifiable'' so we have better be more specific. Ken and I thought a bit about how to shape a more specific testable question, and here is what we came up with-- very tentatively still. Suppose that $N$ and $M$ are distinct prime numbers, and $f$ and $g$ are newforms of weight two on $X_0(N)$ and $X_0(M)$ respectively. Now let $p$ be a prime number (or ideal) dividing either $1+M- a_M(f)$ or $1+M + a_M(f)$, and let $q$ be a prime number (or ideal) dividing either $1+N - a_N(g)$ or $1+N + a_N(g)$. Let us suppose that the residual characteristics of the ideals $p$ and $q$ are distinct (i.e., if we are in a case where $p$ and $q$ are prime numbers, we just want them to be distinct). Suppose also that the corresponding Galois representations associated to $f \mod p$ and $g \mod q$ are irreducible. Let us say that we have ``maximum success'' if for any such choice of $f,g, p, q$ there is a modular newform $h$ of weight two on $X_0(NM)$ which is congruent to $f \mod p$ and to $g \mod q$. Here $a_N(f)$ means the $N$th Fourier coefficient of $f$, etc. The reason why we call the above ``maximum success'' is that we are putting down the ``evident'' conditions necessary for there to be such a newform $h$ (and looking for such an $h$ at the minimal conceivable level, and weight). It is probably unreasonable to expect ``maximum success'', but initial experiments might give us a sense of how far from the mark ``maximal success'' actually is, in which case we will weaken our expectations accordingly... I should also say, that the first case is $N=11$ and $M=17$, where the level of the sought for $h$ is $187$, i.e., not too large yet... Does this sound as if it is a conceivable, fun, etc. computation to make? Barry \begin{verbatim} Date: Mon, 26 Oct 1998 12:46:09 -0500 \end{verbatim} Dear William, That's terrific! Actually I had debated about whether to exclude the prime $2$ from the search-- it being slightly problematic for level-raising, level-lowering issues. I also excluded reducible representations as being significantly more problematic on a number of other grounds. But, while you are systemtically doing the computation, it might make sense not to exclude reducible representations from the search, but just indicate in the data when they are reducible. After all, we may also be getting some ``maximal succeses'' there too (but if we get a "failure" for a reducible case, I wouldn't worry). Keep me posted! Barry \begin{verbatim} Date: Tue, 3 Nov 1998 20:32:35 +0000 (GMT) From: Kevin Buzzard To: was@bmw.autobahn.org Subject: Re: congruence table I looked through your tables a fair bit yesterday and can't find anything which smacks of contradiction, which is very comforting. It all seems to fit together very well, which means that I am getting more and more confident in your programs! [NB my experience with these programs is that if they "usually" work then they still might not work 100% because if numbers get too big then there's weird overflows and so maybe things don't work then--- but I don't have any evidence at all that your programs don't work 100%] Anyway, here's some random comments about them. When you say in the intro that "in _some_ cases the program didn't perform a complete check of congruence"---really, you never performed a _complete_ check. If you mean "complete check up to p=***" whatever *** is, maybe you should say this. Also it's a bit strange that you then go on to talk about the ?? cases, and say that they're congruences with a "high probability", whereas in reality we're *always* only dealing with probabilities (except, I guess, in cases where Ken's theorem predicts that a form exists and only 1 form can possibly work at level NM). In practice it's very difficult to verify that forms are actually congruent because the effective Chebatorev bounds aren't good enough. \end{verbatim} \newpage \textheight=1.28\textheight \textwidth=1.35\textwidth \voffset=-1.3in \hoffset=-.9in \section{Table of Congruences} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=17A}$}\\ \begin{tabular}{|cc|cccccc|}\hline $P$&$Q$&187A&187B&187C&187D&187E&187F\\\hline $2$&$3$&$ f$&$ f$&$ fg$&$ f$&$ f$&$ g$\\\hline $5$&$2$&$ $&$ $&$ $&$ $&$ g$&$ $\\\hline $5$&$3$&$ $&$ $&$ g$&$ $&$ $&$ g$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=19A}$}\\ \begin{tabular}{|cc|cccc|}\hline $P$&$Q$&209A&209B&209C&209D\\\hline $2$&$3$&$ f$&$ f_?$&$ f_?g$&$ fg$\\\hline $2$&$5$&$ f$&$ f_?$&$ f_?g$&$ f$\\\hline $5$&$3$&$ $&$ f$&$ g$&$ g$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=23A}$}\\ \begin{tabular}{|cc|cccc|}\hline $P$&$Q$&253A&253B&253C&253D\\\hline $23$&$({x + {8}},11) $&$ $&$ $&$ $&$ f$\\\hline $23$&$({x + {15}},19) $&$ g$&$ $&$ $&$ f$\\\hline $23$&$({x^{2} + x + 1},2) $&$ $&$ $&$ g$&$ fg$\\\hline $23$&$({x + {3}},5) $&$ $&$ g$&$ $&$ f$\\\hline $5$&$({x + {8}},11) $&$ $&$ f$&$ $&$ $\\\hline $5$&$({x + {15}},19) $&$ g$&$ f$&$ $&$ $\\\hline $5$&$({x^{2} + x + 1},2) $&$ $&$ f$&$ g$&$ g$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=29A}$}\\ \begin{tabular}{|cc|ccccc|}\hline $P$&$Q$&319A&319B&319C&319D&319E\\\hline $2$&$({x + {14}},167) $&$ f$&$ $&$ f$&$ $&$ g$\\\hline $2$&$({x + {7}},17) $&$ f$&$ g$&$ f$&$ $&$ $\\\hline $2$&$({x + {4}},7) $&$ f$&$ $&$ f$&$ $&$ $\\\hline $3$&$({x + {14}},167) $&$ $&$ f$&$ $&$ f$&$ g$\\\hline $3$&$({x + {7}},17) $&$ $&$ fg$&$ $&$ f$&$ $\\\hline $3$&$({x + {4}},7) $&$ $&$ f$&$ $&$ f$&$ $\\\hline $5$&$({x + {14}},167) $&$ $&$ $&$ $&$ f$&$ g$\\\hline $5$&$({x + {7}},17) $&$ $&$ g$&$ $&$ f$&$ $\\\hline $5$&$({x + {4}},7) $&$ $&$ $&$ $&$ f$&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=17A, \, g=19A}$}\\ \begin{tabular}{|cc|cccccc|}\hline $P$&$Q$&323A&323B&323C&323D&323E&323F\\\hline $2$&$3$&$ f$&$ $&$ f$&$ f_?g$&$ f_?$&$ $\\\hline $2$&$5$&$ f$&$ $&$ f$&$ f_?$&$ f_?$&$ g$\\\hline $2$&$7$&$ f$&$ g$&$ f$&$ f_?$&$ f_?$&$ $\\\hline $3$&$5$&$ $&$ f$&$ $&$ $&$ $&$ g$\\\hline $3$&$7$&$ $&$ fg$&$ $&$ $&$ $&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=31A}$}\\ \begin{tabular}{|cc|cccc|}\hline $P$&$Q$&341A&341B&341C&341D\\\hline $13$&$({x^{2} + x + 1},2) $&$ $&$ g_?$&$ $&$ fg_?$\\\hline $13$&$({x + {2}},5) $&$ g$&$ $&$ $&$ f$\\\hline $13$&$({x^{2} + {6}x + {6}},7) $&$ $&$ $&$ g_?$&$ f$\\\hline $3$&$({x^{2} + x + 1},2) $&$ $&$ g_?$&$ $&$ f_?g_?$\\\hline $3$&$({x + {2}},5) $&$ g$&$ $&$ $&$ f_?$\\\hline $3$&$({x^{2} + {6}x + {6}},7) $&$ $&$ $&$ g_?$&$ f_?$\\\hline $5$&$({x^{2} + x + 1},2) $&$ f$&$ g_?$&$ $&$ g_?$\\\hline $5$&$({x^{2} + {6}x + {6}},7) $&$ f$&$ $&$ g_?$&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=17A, \, g=23A}$}\\ \begin{tabular}{|cc|ccccc|}\hline $P$&$Q$&391A&391B&391C&391D&391E\\\hline $2$&$({x + {99}},109) $&$ $&$ $&$ g$&$ $&$ f_?$\\\hline $2$&$({x + {8}},11) $&$ $&$ $&$ $&$ $&$ f_?$\\\hline $2$&$({x + {3}},5) $&$ $&$ g$&$ $&$ $&$ f_?$\\\hline $5$&$({x + {99}},109) $&$ $&$ f$&$ g$&$ $&$ $\\\hline $5$&$({x + {8}},11) $&$ $&$ f$&$ $&$ $&$ $\\\hline $5$&$({x^{2} + x + 1},2) $&$ $&$ f$&$ $&$ g$&$ g_?$\\\hline $7$&$({x + {99}},109) $&$ $&$ $&$ g$&$ $&$ f_?$\\\hline $7$&$({x + {8}},11) $&$ $&$ $&$ $&$ $&$ f_?$\\\hline $7$&$({x^{2} + x + 1},2) $&$ $&$ $&$ $&$ g$&$ f_?g_?$\\\hline $7$&$({x + {3}},5) $&$ $&$ g$&$ $&$ $&$ f_?$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=37A}$}\\ \begin{tabular}{|cc|cccc|}\hline $P$&$Q$&407A&407B&407C&407D\\\hline $41$&$17$&$ $&$ $&$ fg$&$ $\\\hline $41$&$7$&$ g$&$ $&$ f$&$ $\\\hline $5$&$17$&$ $&$ $&$ g$&$ $\\\hline $5$&$7$&$ g$&$ $&$ $&$ $\\\hline $7$&$17$&$ $&$ f$&$ g$&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=37B}$}\\ \begin{tabular}{|cc|cccc|}\hline $P$&$Q$&407A&407B&407C&407D\\\hline $41$&$3$&$ $&$ g$&$ f$&$ g$\\\hline $41$&$5$&$ $&$ $&$ f$&$ g$\\\hline $5$&$3$&$ $&$ g$&$ $&$ g$\\\hline $7$&$3$&$ $&$ fg$&$ $&$ g$\\\hline $7$&$5$&$ $&$ f$&$ $&$ g$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=19A, \, g=23A}$}\\ \begin{tabular}{|cc|cccccccc|}\hline $P$&$Q$&437A&437B&437C&437D&437E&437F&437G&437H\\\hline $2$&$({x + {4}},11) $&$ f$&$ f$&$ g$&$ f$&$ $&$ f_?$&$ f_?$&$ f_?$\\\hline $2$&$({x + {8}},11) $&$ f$&$ f$&$ $&$ f$&$ $&$ f_?$&$ f_?$&$ f_?$\\\hline $2$&$({x^{2} + x + {2}},3) $&$ f$&$ f$&$ $&$ f$&$ $&$ f_?$&$ f_?g$&$ f_?$\\\hline $3$&$({x + {4}},11) $&$ $&$ $&$ g$&$ $&$ $&$ $&$ $&$ f$\\\hline $3$&$({x + {8}},11) $&$ $&$ $&$ $&$ $&$ $&$ $&$ $&$ f$\\\hline $3$&$({x^{2} + x + 1},2) $&$ $&$ $&$ $&$ $&$ $&$ g_?$&$ $&$ fg_?$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=41A}$} {\small (char 2 primes for $g$ omitted)}\\ \begin{tabular}{|cc|ccccc|}\hline $P$&$Q$&451A&451B&451C&451D&451E\\\hline $17$&$({x + {2}},5) $&$ $&$ g$&$ f$&$ $&$ $\\\hline $17$&$({x + {413}},863) $&$ $&$ $&$ f$&$ g$&$ $\\\hline $2$&$({x + {2}},5) $&$ $&$ g$&$ $&$ f_?$&$ f$\\\hline $2$&$({x + {413}},863) $&$ $&$ $&$ $&$ f_?g$&$ f$\\\hline $5$&$({x + {413}},863) $&$ $&$ f$&$ $&$ g$&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=43A}$}\\ \begin{tabular}{|cc|ccccccc|}\hline $P$&$Q$&473A&473B&473C&473D&473E&473F&473G\\\hline $19$&$3$&$ $&$ $&$ $&$ $&$ $&$ fg$&$ g$\\\hline $19$&$5$&$ $&$ g$&$ $&$ $&$ $&$ f$&$ $\\\hline $2$&$3$&$ $&$ $&$ $&$ $&$ f_?$&$ g$&$ fg$\\\hline $2$&$5$&$ $&$ g$&$ $&$ $&$ f_?$&$ $&$ f$\\\hline $5$&$3$&$ f$&$ $&$ $&$ $&$ $&$ g$&$ g$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=43B}$}\\ \begin{tabular}{|cc|ccccccc|}\hline $P$&$Q$&473A&473B&473C&473D&473E&473F&473G\\\hline $19$&$({x + {62}},113) $&$ $&$ $&$ $&$ $&$ g$&$ f$&$ $\\\hline $19$&$({x + {5}},23) $&$ $&$ $&$ g$&$ $&$ $&$ f$&$ $\\\hline $19$&$({x + {4}},7) $&$ $&$ $&$ $&$ $&$ $&$ f$&$ $\\\hline $2$&$({x + {62}},113) $&$ $&$ $&$ $&$ $&$ f_?g$&$ $&$ f$\\\hline $2$&$({x + {5}},23) $&$ $&$ $&$ g$&$ $&$ f_?$&$ $&$ f$\\\hline $2$&$({x + {4}},7) $&$ $&$ $&$ $&$ $&$ f_?$&$ $&$ f$\\\hline $5$&$({x + {62}},113) $&$ f$&$ $&$ $&$ $&$ g$&$ $&$ $\\\hline $5$&$({x + {5}},23) $&$ f$&$ $&$ g$&$ $&$ $&$ $&$ $\\\hline $5$&$({x + {4}},7) $&$ f$&$ $&$ $&$ $&$ $&$ $&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=17A, \, g=29A}$}\\ \begin{tabular}{|cc|cccccccc|}\hline $P$&$Q$&493A&493B&493C&493D&493E&493F&493G&493H\\\hline $2$&$({x + {24}},31) $&$ $&$ $&$ $&$ $&$ f$&$ f$&$ f_?g$&$ $\\\hline $2$&$({x + {4}},7) $&$ $&$ $&$ $&$ g$&$ f$&$ f$&$ f_?$&$ $\\\hline $3$&$({x + 1},2) $&$ fg$&$ g$&$ g$&$ $&$ $&$ g$&$ $&$ f$\\\hline $3$&$({x + {24}},31) $&$ f$&$ $&$ $&$ $&$ $&$ $&$ g$&$ f$\\\hline $3$&$({x + {4}},7) $&$ f$&$ $&$ $&$ g$&$ $&$ $&$ $&$ f$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=47A}$}\\ \begin{tabular}{|cc|ccccccccccc|}\hline $P$&$Q$&517A&517B&517C&517D&517E&517F&517G&517H&517I&517J&517K\\\hline $2$&$({x + {20}},23) $&$ f$&$ f$&$ f_?$&$ $&$ $&$ f_?$&$ $&$ $&$ f_?$&$ f_?$&$ f$\\\hline $2$&$({x + 1},3) $&$ f$&$ fg$&$ f_?$&$ $&$ $&$ f_?g$&$ $&$ g_?$&$ f_?$&$ f_?$&$ fg$\\\hline $2$&$({x + {8}},31) $&$ f$&$ f$&$ f_?g$&$ $&$ $&$ f_?$&$ $&$ $&$ f_?$&$ f_?$&$ f$\\\hline $2$&$({x + {2}},7) $&$ f$&$ f$&$ f_?$&$ g$&$ $&$ f_?$&$ $&$ $&$ f_?$&$ f_?$&$ f$\\\hline $5$&$({x^{4} + x^{3} + x^{2} + x + 1},2) $&$ $&$ $&$ $&$ $&$ $&$ $&$ $&$ $&$ g_?$&$ g_?$&$ $\\\hline $5$&$({x + {20}},23) $&$ $&$ $&$ $&$ $&$ $&$ $&$ $&$ $&$ $&$ $&$ $\\\hline $5$&$({x + 1},3) $&$ $&$ g$&$ $&$ $&$ $&$ g$&$ $&$ g_?$&$ $&$ $&$ g$\\\hline $5$&$({x + {8}},31) $&$ $&$ $&$ g$&$ $&$ $&$ $&$ $&$ $&$ $&$ $&$ $\\\hline $5$&$({x + {2}},7) $&$ $&$ $&$ $&$ g$&$ $&$ $&$ $&$ $&$ $&$ $&$ $\\\hline $7$&$({x^{4} + x^{3} + x^{2} + x + 1},2) $&$ $&$ $&$ $&$ $&$ f$&$ $&$ $&$ $&$ g_?$&$ g_?$&$ $\\\hline $7$&$({x + {20}},23) $&$ $&$ $&$ $&$ $&$ f$&$ $&$ $&$ $&$ $&$ $&$ $\\\hline $7$&$({x + 1},3) $&$ $&$ g$&$ $&$ $&$ f$&$ g$&$ $&$ g_?$&$ $&$ $&$ g$\\\hline $7$&$({x + {8}},31) $&$ $&$ $&$ g$&$ $&$ f$&$ $&$ $&$ $&$ $&$ $&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=17A, \, g=31A}$}\\ \begin{tabular}{|cc|ccccc|}\hline $P$&$Q$&527A&527B&527C&527D&527E\\\hline $2$&$({x + {98}},109) $&$ $&$ $&$ $&$ g$&$ f_?$\\\hline $2$&$({x + {7}},11) $&$ g$&$ $&$ $&$ $&$ f_?$\\\hline $2$&$({x + {2}},5) $&$ $&$ $&$ $&$ $&$ f_?$\\\hline $3$&$({x + {98}},109) $&$ $&$ $&$ $&$ g$&$ f_?$\\\hline $3$&$({x + {7}},11) $&$ g$&$ $&$ $&$ $&$ f_?$\\\hline $3$&$({x^{2} + x + 1},2) $&$ $&$ $&$ g$&$ $&$ f_?g_?$\\\hline $3$&$({x + {2}},5) $&$ $&$ $&$ $&$ $&$ f_?$\\\hline $7$&$({x + {98}},109) $&$ f$&$ $&$ $&$ g$&$ $\\\hline $7$&$({x + {7}},11) $&$ fg$&$ $&$ $&$ $&$ $\\\hline $7$&$({x^{2} + x + 1},2) $&$ f$&$ $&$ g$&$ $&$ g_?$\\\hline $7$&$({x + {2}},5) $&$ f$&$ $&$ $&$ $&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=19A, \, g=29A}$}\\ \begin{tabular}{|cc|cccccccc|}\hline $P$&$Q$&551A&551B&551C&551D&551E&551F&551G&551H\\\hline $2$&$({x^{2} + {2}x + {12}},13) $&$ $&$ f$&$ f$&$ $&$ f$&$ f_?$&$ f_?g$&$ $\\\hline $2$&$({x + {4}},7) $&$ $&$ f$&$ f$&$ $&$ f$&$ f_?$&$ f_?$&$ $\\\hline $2$&$({x + {5}},7) $&$ $&$ f$&$ fg$&$ $&$ f$&$ f_?$&$ f_?$&$ $\\\hline $3$&$({x^{2} + {2}x + {12}},13) $&$ $&$ $&$ $&$ $&$ $&$ f_?$&$ g$&$ $\\\hline $3$&$({x + 1},2) $&$ g$&$ $&$ $&$ g$&$ $&$ f_?g_?$&$ g_?$&$ g$\\\hline $3$&$({x + {4}},7) $&$ $&$ $&$ $&$ $&$ $&$ f_?$&$ $&$ $\\\hline $3$&$({x + {5}},7) $&$ $&$ $&$ g$&$ $&$ $&$ f_?$&$ $&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=53A}$}\\ \begin{tabular}{|cc|ccccccccc|}\hline $P$&$Q$&583A&583B&583C&583D&583E&583F&583G&583H&583I\\\hline $2$&$3$&$ $&$ f$&$ fg$&$ f$&$ fg$&$ $&$ f_?$&$ f_?$&$ f_?$\\\hline $3$&$2$&$ fg$&$ $&$ $&$ $&$ $&$ g_?$&$ f$&$ g_?$&$ $\\\hline $5$&$2$&$ g$&$ $&$ $&$ $&$ $&$ g_?$&$ $&$ g_?$&$ $\\\hline $5$&$3$&$ $&$ $&$ g$&$ $&$ g$&$ $&$ $&$ $&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=53B}$}\\ \begin{tabular}{|cc|ccccccccc|}\hline $P$&$Q$&583A&583B&583C&583D&583E&583F&583G&583H&583I\\\hline $2$&$({x + {10}},13) $&$ $&$ f$&$ f$&$ f$&$ f$&$ $&$ f_?$&$ f_?$&$ f_?$\\\hline $2$&$({x + {224}},281) $&$ $&$ f$&$ f$&$ f$&$ f$&$ $&$ f_?$&$ f_?$&$ f_?g$\\\hline $2$&$({x + {5}},43) $&$ $&$ f$&$ f$&$ f$&$ f$&$ $&$ f_?g$&$ f_?$&$ f_?$\\\hline $3$&$({x + {10}},13) $&$ f$&$ $&$ $&$ $&$ $&$ $&$ f$&$ $&$ $\\\hline $3$&$({x + 1},2) $&$ fg$&$ $&$ $&$ $&$ $&$ g_?$&$ f$&$ g_?$&$ $\\\hline $3$&$({x + {224}},281) $&$ f$&$ $&$ $&$ $&$ $&$ $&$ f$&$ $&$ g$\\\hline $3$&$({x + {5}},43) $&$ f$&$ $&$ $&$ $&$ $&$ $&$ fg$&$ $&$ $\\\hline $5$&$({x + {10}},13) $&$ $&$ $&$ $&$ $&$ $&$ $&$ $&$ $&$ $\\\hline $5$&$({x + 1},2) $&$ g$&$ $&$ $&$ $&$ $&$ g_?$&$ $&$ g_?$&$ $\\\hline $5$&$({x + {224}},281) $&$ $&$ $&$ $&$ $&$ $&$ $&$ $&$ $&$ g$\\\hline $5$&$({x + {5}},43) $&$ $&$ $&$ $&$ $&$ $&$ $&$ g$&$ $&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=19A, \, g=31A}$}\\ \begin{tabular}{|cc|ccccc|}\hline $P$&$Q$&589A&589B&589C&589D&589E\\\hline $2$&$({x + {2}},5) $&$ $&$ f$&$ f$&$ f_?g$&$ f$\\\hline $2$&$({x + {29}},79) $&$ $&$ f$&$ f$&$ f_?g$&$ f$\\\hline $2$&$({x + {49}},79) $&$ $&$ f$&$ f$&$ f_?$&$ fg$\\\hline $3$&$({x + {2}},5) $&$ $&$ $&$ $&$ g$&$ f$\\\hline $3$&$({x + {29}},79) $&$ $&$ $&$ $&$ g$&$ f$\\\hline $3$&$({x + {49}},79) $&$ $&$ $&$ $&$ $&$ fg$\\\hline $7$&$({x + {2}},5) $&$ f$&$ $&$ $&$ g$&$ $\\\hline $7$&$({x + {29}},79) $&$ f$&$ $&$ $&$ g$&$ $\\\hline $7$&$({x + {49}},79) $&$ f$&$ $&$ $&$ $&$ g$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=17A, \, g=37A}$}\\ \begin{tabular}{|cc|cccccccc|}\hline $P$&$Q$&629A&629B&629C&629D&629E&629F&629G&629H\\\hline $2$&$3$&$ g$&$ $&$ $&$ $&$ f_?$&$ f_?g$&$ fg$&$ $\\\hline $3$&$2$&$ $&$ $&$ fg$&$ $&$ g_?$&$ f$&$ g$&$ g$\\\hline $5$&$2$&$ $&$ f$&$ g$&$ $&$ g_?$&$ $&$ g$&$ g$\\\hline $5$&$3$&$ g$&$ f$&$ $&$ $&$ $&$ g$&$ g$&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=17A, \, g=37B}$}\\ \begin{tabular}{|cc|cccccccc|}\hline $P$&$Q$&629A&629B&629C&629D&629E&629F&629G&629H\\\hline $2$&$3$&$ $&$ $&$ $&$ $&$ f_?g$&$ f_?$&$ f$&$ $\\\hline $3$&$2$&$ $&$ $&$ fg$&$ $&$ g_?$&$ f$&$ g$&$ g$\\\hline $5$&$2$&$ $&$ f$&$ g$&$ $&$ g_?$&$ $&$ g$&$ g$\\\hline $5$&$3$&$ $&$ f$&$ $&$ $&$ g$&$ $&$ $&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=59A}$} {\small (char 2 primes for $g$ omitted)}\\ \begin{tabular}{|cc|cccccc|}\hline $P$&$Q$&649A&649B&649C&649D&649E&649F\\\hline $11$&$({x + {9}},19) $&$ $&$ $&$ fg$&$ $&$ $&$ $\\\hline $11$&$({x + {1940}},2671) $&$ $&$ $&$ f$&$ g$&$ $&$ $\\\hline $11$&$({x + {26}},29) $&$ $&$ $&$ f$&$ $&$ $&$ $\\\hline $11$&$({x + 1},7) $&$ $&$ g$&$ f$&$ $&$ $&$ $\\\hline $13$&$({x + {9}},19) $&$ $&$ $&$ g$&$ $&$ f$&$ $\\\hline $13$&$({x + {1940}},2671) $&$ $&$ $&$ $&$ g$&$ f$&$ $\\\hline $13$&$({x + {26}},29) $&$ $&$ $&$ $&$ $&$ f$&$ $\\\hline $13$&$({x + 1},7) $&$ $&$ g$&$ $&$ $&$ f$&$ $\\\hline $5$&$({x + {9}},19) $&$ $&$ $&$ g$&$ $&$ f$&$ $\\\hline $5$&$({x + {1940}},2671) $&$ $&$ $&$ $&$ g$&$ f$&$ $\\\hline $5$&$({x + {26}},29) $&$ $&$ $&$ $&$ $&$ f$&$ $\\\hline $5$&$({x + 1},7) $&$ $&$ g$&$ $&$ $&$ f$&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=23A, \, g=29A}$}\\ \begin{tabular}{|cc|cccc|}\hline $P$&$Q$&667A&667B&667C&667D\\\hline $({x + {4}},11) $&$({x + {52}},113) $&$ f$&$ $&$ $&$ g$\\\hline $({x + {4}},11) $&$({x + 1},2) $&$ f$&$ g$&$ g_?$&$ $\\\hline $({x + {4}},11) $&$({x + {19}},23) $&$ fg$&$ $&$ $&$ $\\\hline $({x + {4}},11) $&$({x + {4}},7) $&$ f$&$ $&$ $&$ $\\\hline $({x + {8}},11) $&$({x + {52}},113) $&$ $&$ $&$ $&$ g$\\\hline $({x + {8}},11) $&$({x + 1},2) $&$ $&$ g$&$ g_?$&$ $\\\hline $({x + {8}},11) $&$({x + {19}},23) $&$ g$&$ $&$ $&$ $\\\hline $({x + {8}},11) $&$({x + {4}},7) $&$ $&$ $&$ $&$ $\\\hline $({x^{2} + x + {2}},3) $&$({x + {52}},113) $&$ f$&$ $&$ f$&$ g$\\\hline $({x^{2} + x + {2}},3) $&$({x + 1},2) $&$ f$&$ g$&$ fg_?$&$ $\\\hline $({x^{2} + x + {2}},3) $&$({x + {19}},23) $&$ fg$&$ $&$ f$&$ $\\\hline $({x^{2} + x + {2}},3) $&$({x + {4}},7) $&$ f$&$ $&$ f$&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=61A}$}\\ \begin{tabular}{|cc|cccc|}\hline $P$&$Q$&671A&671B&671C&671D\\\hline $2$&$17$&$ $&$ f$&$ f$&$ g$\\\hline $2$&$7$&$ $&$ fg$&$ f$&$ $\\\hline $37$&$17$&$ $&$ $&$ $&$ fg$\\\hline $37$&$7$&$ $&$ g$&$ $&$ f$\\\hline $5$&$17$&$ f$&$ $&$ $&$ g$\\\hline $5$&$7$&$ f$&$ g$&$ $&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=61B}$}\\ \begin{tabular}{|cc|cccc|}\hline $P$&$Q$&671A&671B&671C&671D\\\hline $2$&$({x + {3}},13) $&$ $&$ f$&$ fg$&$ $\\\hline $2$&$({x + {9}},17) $&$ g$&$ f$&$ f$&$ $\\\hline $2$&$({x + {16}},331) $&$ $&$ f$&$ fg$&$ $\\\hline $2$&$({x + {2}},5) $&$ g$&$ f$&$ f$&$ $\\\hline $37$&$({x + {3}},13) $&$ $&$ $&$ g$&$ f$\\\hline $37$&$({x + {9}},17) $&$ g$&$ $&$ $&$ f$\\\hline $37$&$({x + {16}},331) $&$ $&$ $&$ g$&$ f$\\\hline $37$&$({x + {2}},5) $&$ g$&$ $&$ $&$ f$\\\hline $5$&$({x + {3}},13) $&$ f$&$ $&$ g$&$ $\\\hline $5$&$({x + {9}},17) $&$ fg$&$ $&$ $&$ $\\\hline $5$&$({x + {16}},331) $&$ f$&$ $&$ g$&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=17A, \, g=41A}$} {\small (char 2 primes for $g$ omitted)}\\ \begin{tabular}{|cc|cccccc|}\hline $P$&$Q$&697A&697B&697C&697D&697E&697F\\\hline $2$&$({x + {2}},5) $&$ f$&$ f_?$&$ f$&$ $&$ f_?$&$ f_?$\\\hline $2$&$({x^{2} + {4}x + {2}},5) $&$ f$&$ f_?$&$ f$&$ g$&$ f_?$&$ f_?$\\\hline $3$&$({x + {2}},5) $&$ f$&$ $&$ $&$ $&$ f$&$ $\\\hline $3$&$({x^{2} + {4}x + {2}},5) $&$ f$&$ $&$ $&$ g$&$ f$&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=19A, \, g=37A}$}\\ \begin{tabular}{|cc|ccccccccc|}\hline $P$&$Q$&703A&703B&703C&703D&703E&703F&703G&703H&703I\\\hline $2$&$5$&$ f$&$ $&$ $&$ $&$ $&$ f_?$&$ fg$&$ f_?g$&$ $\\\hline $3$&$2$&$ $&$ g$&$ g$&$ f$&$ g$&$ g_?$&$ $&$ g_?$&$ g$\\\hline $3$&$5$&$ $&$ $&$ $&$ f$&$ $&$ $&$ g$&$ g$&$ $\\\hline $5$&$2$&$ $&$ g$&$ g$&$ $&$ g$&$ g_?$&$ $&$ g_?$&$ fg$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=19A, \, g=37B}$}\\ \begin{tabular}{|cc|ccccccccc|}\hline $P$&$Q$&703A&703B&703C&703D&703E&703F&703G&703H&703I\\\hline $2$&$11$&$ f$&$ $&$ $&$ $&$ $&$ f_?g$&$ f$&$ f_?$&$ $\\\hline $2$&$3$&$ f$&$ $&$ $&$ g$&$ $&$ f_?$&$ f$&$ f_?$&$ $\\\hline $3$&$11$&$ $&$ $&$ $&$ f$&$ $&$ g$&$ $&$ $&$ $\\\hline $3$&$2$&$ $&$ g$&$ g$&$ f$&$ g$&$ g_?$&$ $&$ g_?$&$ g$\\\hline $5$&$11$&$ $&$ $&$ $&$ $&$ $&$ g$&$ $&$ $&$ f$\\\hline $5$&$2$&$ $&$ g$&$ g$&$ $&$ g$&$ g_?$&$ $&$ g_?$&$ fg$\\\hline $5$&$3$&$ $&$ $&$ $&$ g$&$ $&$ $&$ $&$ $&$ f$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=23A, \, g=31A}$}\\ \begin{tabular}{|cc|ccccccc|}\hline $P$&$Q$&713A&713B&713C&713D&713E&713F&713G\\\hline $({x + {4}},11) $&$({x^{2} + x + 1},2) $&$ $&$ g$&$ $&$ $&$ fg_?$&$ $&$ $\\\hline $({x + {4}},11) $&$({x + {5}},29) $&$ $&$ $&$ $&$ $&$ f$&$ $&$ g$\\\hline $({x + {4}},11) $&$({x + {2}},5) $&$ $&$ $&$ $&$ $&$ f$&$ $&$ $\\\hline $({x + {8}},11) $&$({x^{2} + x + 1},2) $&$ $&$ g$&$ $&$ $&$ g_?$&$ $&$ $\\\hline $({x + {8}},11) $&$({x + {5}},29) $&$ $&$ $&$ $&$ $&$ $&$ $&$ g$\\\hline $({x + {8}},11) $&$({x + {2}},5) $&$ $&$ $&$ $&$ $&$ $&$ $&$ $\\\hline $({x + {10}},89) $&$({x + {7}},11) $&$ $&$ $&$ $&$ g$&$ $&$ $&$ f$\\\hline $({x + {10}},89) $&$({x^{2} + x + 1},2) $&$ $&$ g$&$ $&$ $&$ g_?$&$ $&$ f$\\\hline $({x + {10}},89) $&$({x + {5}},29) $&$ $&$ $&$ $&$ $&$ $&$ $&$ fg$\\\hline $({x + {10}},89) $&$({x + {2}},5) $&$ $&$ $&$ $&$ $&$ $&$ $&$ f$\\\hline $({x + {80}},89) $&$({x + {7}},11) $&$ $&$ $&$ $&$ g$&$ f_?$&$ $&$ $\\\hline $({x + {80}},89) $&$({x^{2} + x + 1},2) $&$ $&$ g$&$ $&$ $&$ f_?g_?$&$ $&$ $\\\hline $({x + {80}},89) $&$({x + {5}},29) $&$ $&$ $&$ $&$ $&$ f_?$&$ $&$ g$\\\hline $({x + {80}},89) $&$({x + {2}},5) $&$ $&$ $&$ $&$ $&$ f_?$&$ $&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=17A, \, g=43A}$}\\ \begin{tabular}{|cc|cccccc|}\hline $P$&$Q$&731A&731B&731C&731D&731E&731F\\\hline $2$&$3$&$ g$&$ f$&$ $&$ $&$ f_?$&$ f_?g_?$\\\hline $2$&$5$&$ $&$ f$&$ g$&$ $&$ f_?$&$ f_?$\\\hline $2$&$7$&$ $&$ f$&$ $&$ $&$ f_?$&$ f_?g$\\\hline $3$&$5$&$ $&$ $&$ g$&$ $&$ $&$ f_?$\\\hline $3$&$7$&$ $&$ $&$ $&$ $&$ $&$ f_?g$\\\hline $5$&$3$&$ g$&$ $&$ $&$ f$&$ $&$ g_?$\\\hline $5$&$7$&$ $&$ $&$ $&$ f$&$ $&$ g$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=17A, \, g=43B}$}\\ \begin{tabular}{|cc|cccccc|}\hline $P$&$Q$&731A&731B&731C&731D&731E&731F\\\hline $2$&$({x + {5}},23) $&$ $&$ f$&$ $&$ g$&$ f_?$&$ f_?$\\\hline $2$&$({x + {272}},521) $&$ $&$ f$&$ $&$ $&$ f_?g$&$ f_?$\\\hline $2$&$({x + {4}},7) $&$ $&$ f$&$ $&$ $&$ f_?$&$ f_?$\\\hline $3$&$({x + {5}},23) $&$ $&$ $&$ $&$ g$&$ $&$ f_?$\\\hline $3$&$({x + {272}},521) $&$ $&$ $&$ $&$ $&$ g$&$ f_?$\\\hline $3$&$({x + {4}},7) $&$ $&$ $&$ $&$ $&$ $&$ f_?$\\\hline $5$&$({x + {5}},23) $&$ $&$ $&$ $&$ fg$&$ $&$ $\\\hline $5$&$({x + {272}},521) $&$ $&$ $&$ $&$ f$&$ g$&$ $\\\hline $5$&$({x + {4}},7) $&$ $&$ $&$ $&$ f$&$ $&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=67A}$}\\ \begin{tabular}{|cc|cccccc|}\hline $P$&$Q$&737A&737B&737C&737D&737E&737F\\\hline $3$&$2$&$ fg$&$ g$&$ g_?$&$ g$&$ g_?$&$ $\\\hline $5$&$2$&$ g$&$ g$&$ g_?$&$ g$&$ g_?$&$ f$\\\hline $61$&$2$&$ g$&$ g$&$ fg_?$&$ g$&$ g_?$&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=67B}$}\\ \begin{tabular}{|cc|cccccc|}\hline $P$&$Q$&737A&737B&737C&737D&737E&737F\\\hline $3$&$({x + {4}},11) $&$ f$&$ $&$ $&$ $&$ $&$ g$\\\hline $3$&$({x + {8}},11) $&$ f$&$ $&$ $&$ $&$ $&$ $\\\hline $3$&$({x^{2} + x + {12}},13) $&$ f$&$ $&$ $&$ $&$ g$&$ $\\\hline $5$&$({x + {4}},11) $&$ $&$ $&$ $&$ $&$ $&$ fg$\\\hline $5$&$({x + {8}},11) $&$ $&$ $&$ $&$ $&$ $&$ f$\\\hline $5$&$({x^{2} + x + {12}},13) $&$ $&$ $&$ $&$ $&$ g$&$ f$\\\hline $61$&$({x + {4}},11) $&$ $&$ $&$ f$&$ $&$ $&$ g$\\\hline $61$&$({x + {8}},11) $&$ $&$ $&$ f$&$ $&$ $&$ $\\\hline $61$&$({x^{2} + x + {12}},13) $&$ $&$ $&$ f$&$ $&$ g$&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=67C}$}\\ \begin{tabular}{|cc|cccccc|}\hline $P$&$Q$&737A&737B&737C&737D&737E&737F\\\hline $3$&$({x + {65}},139) $&$ f$&$ $&$ $&$ g$&$ $&$ $\\\hline $3$&$({x + {77}},139) $&$ f$&$ $&$ g$&$ $&$ $&$ $\\\hline $5$&$({x + {65}},139) $&$ $&$ $&$ $&$ g$&$ $&$ f$\\\hline $5$&$({x + {77}},139) $&$ $&$ $&$ g$&$ $&$ $&$ f$\\\hline $61$&$({x + {65}},139) $&$ $&$ $&$ f$&$ g$&$ $&$ $\\\hline $61$&$({x + {77}},139) $&$ $&$ $&$ fg$&$ $&$ $&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=19A, \, g=41A}$} {\small (char 2 primes for $g$ omitted)}\\ \begin{tabular}{|cc|ccccc|}\hline $P$&$Q$&779A&779B&779C&779D&779E\\\hline $2$&$({x + {2}},5) $&$ f$&$ f$&$ f$&$ f_?$&$ f_?g_?$\\\hline $2$&$({x + {171}},607) $&$ f$&$ fg$&$ f$&$ f_?$&$ f_?$\\\hline $2$&$({x + {299}},929) $&$ f$&$ f$&$ f$&$ f_?$&$ f_?g$\\\hline $3$&$({x + {2}},5) $&$ $&$ $&$ $&$ f$&$ g_?$\\\hline $3$&$({x + {171}},607) $&$ $&$ g$&$ $&$ f$&$ $\\\hline $3$&$({x + {299}},929) $&$ $&$ $&$ $&$ f$&$ g$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=71A}$}\\ \begin{tabular}{|cc|ccccccc|}\hline $P$&$Q$&781A&781B&781C&781D&781E&781F&781G\\\hline $23$&$({x^{3} + x + 1},2) $&$ $&$ $&$ $&$ $&$ g_?$&$ $&$ fg_?$\\\hline $23$&$({x},3) $&$ g$&$ g$&$ g$&$ g$&$ $&$ $&$ f$\\\hline $23$&$({x + {2}},5) $&$ $&$ $&$ $&$ g$&$ $&$ $&$ f$\\\hline $23$&$({x + {20}},53) $&$ $&$ $&$ $&$ $&$ $&$ g$&$ f$\\\hline $3$&$({x^{3} + x + 1},2) $&$ $&$ $&$ f$&$ $&$ g_?$&$ $&$ f_?g_?$\\\hline $3$&$({x + {2}},5) $&$ $&$ $&$ f$&$ g$&$ $&$ $&$ f_?$\\\hline $3$&$({x + {20}},53) $&$ $&$ $&$ f$&$ $&$ $&$ g$&$ f_?$\\\hline $5$&$({x^{3} + x + 1},2) $&$ $&$ $&$ $&$ f$&$ g_?$&$ $&$ g_?$\\\hline $5$&$({x},3) $&$ g$&$ g$&$ g$&$ fg$&$ $&$ $&$ $\\\hline $5$&$({x + {20}},53) $&$ $&$ $&$ $&$ f$&$ $&$ g$&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=71B}$}\\ \begin{tabular}{|cc|ccccccc|}\hline $P$&$Q$&781A&781B&781C&781D&781E&781F&781G\\\hline $23$&$({x^{3} + x^{2} + 1},2) $&$ $&$ $&$ $&$ $&$ g_?$&$ $&$ fg_?$\\\hline $23$&$({x},3) $&$ g$&$ g$&$ g$&$ g$&$ $&$ $&$ f$\\\hline $23$&$({x + {27}},61) $&$ $&$ $&$ $&$ $&$ $&$ g_?$&$ f$\\\hline $23$&$({x + {4}},7) $&$ $&$ $&$ $&$ $&$ $&$ $&$ f$\\\hline $3$&$({x^{3} + x^{2} + 1},2) $&$ $&$ $&$ f$&$ $&$ g_?$&$ $&$ f_?g_?$\\\hline $3$&$({x + {27}},61) $&$ $&$ $&$ f$&$ $&$ $&$ g_?$&$ f_?$\\\hline $3$&$({x + {4}},7) $&$ $&$ $&$ f$&$ $&$ $&$ $&$ f_?$\\\hline $5$&$({x^{3} + x^{2} + 1},2) $&$ $&$ $&$ $&$ f$&$ g_?$&$ $&$ g_?$\\\hline $5$&$({x},3) $&$ g$&$ g$&$ g$&$ fg$&$ $&$ $&$ $\\\hline $5$&$({x + {27}},61) $&$ $&$ $&$ $&$ f$&$ $&$ g_?$&$ $\\\hline $5$&$({x + {4}},7) $&$ $&$ $&$ $&$ f$&$ $&$ $&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=17A, \, g=47A}$}\\ \begin{tabular}{|cc|ccccccc|}\hline $P$&$Q$&799A&799B&799C&799D&799E&799F&799G\\\hline $2$&$({x + {20}},23) $&$ f$&$ $&$ f$&$ f_?$&$ $&$ f_?$&$ f$\\\hline $2$&$({x + 1},3) $&$ f$&$ $&$ f$&$ f_?g_?$&$ $&$ f_?$&$ fg$\\\hline $2$&$({x + {3495}},43991) $&$ f$&$ $&$ f$&$ f_?g$&$ $&$ f_?$&$ f$\\\hline $2$&$({x + {55}},937) $&$ f$&$ $&$ f$&$ f_?$&$ g$&$ f_?$&$ f$\\\hline $3$&$({x + {20}},23) $&$ $&$ $&$ $&$ $&$ f$&$ f$&$ $\\\hline $3$&$({x + {3495}},43991) $&$ $&$ $&$ $&$ g$&$ f$&$ f$&$ $\\\hline $3$&$({x + {55}},937) $&$ $&$ $&$ $&$ $&$ fg$&$ f$&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=73A}$}\\ \begin{tabular}{|cc|cccccc|}\hline $P$&$Q$&803A&803B&803C&803D&803E&803F\\\hline $13$&$2$&$ $&$ $&$ f$&$ g_?$&$ $&$ $\\\hline $13$&$5$&$ $&$ $&$ f$&$ g$&$ $&$ $\\\hline $13$&$7$&$ $&$ $&$ f$&$ $&$ $&$ g$\\\hline $2$&$5$&$ $&$ f$&$ $&$ f_?g$&$ f$&$ $\\\hline $2$&$7$&$ $&$ f$&$ $&$ $&$ f$&$ g$\\\hline $3$&$2$&$ $&$ $&$ f_?$&$ g_?$&$ $&$ $\\\hline $3$&$5$&$ $&$ $&$ f_?$&$ g$&$ $&$ $\\\hline $3$&$7$&$ $&$ $&$ f_?$&$ $&$ $&$ g$\\\hline $5$&$2$&$ $&$ $&$ $&$ g_?$&$ $&$ $\\\hline $5$&$7$&$ $&$ $&$ $&$ $&$ $&$ g$\\\hline $7$&$2$&$ $&$ $&$ $&$ g_?$&$ $&$ f$\\\hline $7$&$5$&$ $&$ $&$ $&$ g$&$ $&$ f$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=73B}$}\\ \begin{tabular}{|cc|cccccc|}\hline $P$&$Q$&803A&803B&803C&803D&803E&803F\\\hline $13$&$({x + {14}},23) $&$ $&$ $&$ f$&$ $&$ $&$ g$\\\hline $13$&$({x},3) $&$ $&$ g$&$ f$&$ $&$ $&$ $\\\hline $13$&$({x + {15}},79) $&$ $&$ $&$ f$&$ g$&$ $&$ $\\\hline $2$&$({x + {14}},23) $&$ $&$ f$&$ $&$ $&$ f$&$ g$\\\hline $2$&$({x},3) $&$ $&$ fg$&$ $&$ $&$ f$&$ $\\\hline $2$&$({x + {15}},79) $&$ $&$ f$&$ $&$ g$&$ f$&$ $\\\hline $3$&$({x + {14}},23) $&$ $&$ $&$ f_?$&$ $&$ $&$ g$\\\hline $3$&$({x + {15}},79) $&$ $&$ $&$ f_?$&$ g$&$ $&$ $\\\hline $5$&$({x + {14}},23) $&$ $&$ $&$ $&$ $&$ $&$ g$\\\hline $5$&$({x},3) $&$ $&$ g$&$ $&$ $&$ $&$ $\\\hline $5$&$({x + {15}},79) $&$ $&$ $&$ $&$ g$&$ $&$ $\\\hline $7$&$({x + {14}},23) $&$ $&$ $&$ $&$ $&$ $&$ fg$\\\hline $7$&$({x},3) $&$ $&$ g$&$ $&$ $&$ $&$ f$\\\hline $7$&$({x + {15}},79) $&$ $&$ $&$ $&$ g$&$ $&$ f$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=73C}$}\\ \begin{tabular}{|cc|cccccc|}\hline $P$&$Q$&803A&803B&803C&803D&803E&803F\\\hline $13$&$({x + {100}},109) $&$ $&$ $&$ f$&$ $&$ g$&$ $\\\hline $13$&$({x + {15}},181) $&$ $&$ $&$ fg$&$ $&$ $&$ $\\\hline $2$&$({x + {100}},109) $&$ $&$ f$&$ $&$ $&$ fg$&$ $\\\hline $2$&$({x + {15}},181) $&$ $&$ f$&$ g$&$ $&$ f$&$ $\\\hline $3$&$({x + {100}},109) $&$ $&$ $&$ f_?$&$ $&$ g$&$ $\\\hline $3$&$({x + {15}},181) $&$ $&$ $&$ f_?g$&$ $&$ $&$ $\\\hline $5$&$({x + {100}},109) $&$ $&$ $&$ $&$ $&$ g$&$ $\\\hline $5$&$({x + {15}},181) $&$ $&$ $&$ g$&$ $&$ $&$ $\\\hline $7$&$({x + {100}},109) $&$ $&$ $&$ $&$ $&$ g$&$ f$\\\hline $7$&$({x + {15}},181) $&$ $&$ $&$ g$&$ $&$ $&$ f$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=19A, \, g=43A}$}\\ \begin{tabular}{|cc|cccccc|}\hline $P$&$Q$&817A&817B&817C&817D&817E&817F\\\hline $3$&$11$&$ $&$ $&$ f_?$&$ $&$ $&$ g_?$\\\hline $3$&$2$&$ g$&$ g$&$ f_?$&$ g_?$&$ $&$ g_?$\\\hline $43$&$11$&$ $&$ $&$ $&$ $&$ $&$ fg_?$\\\hline $43$&$2$&$ g$&$ g$&$ $&$ g_?$&$ $&$ fg_?$\\\hline $43$&$3$&$ $&$ $&$ $&$ g$&$ $&$ f$\\\hline $5$&$11$&$ f$&$ $&$ $&$ $&$ $&$ g_?$\\\hline $5$&$2$&$ fg$&$ g$&$ $&$ g_?$&$ $&$ g_?$\\\hline $5$&$3$&$ f$&$ $&$ $&$ g$&$ $&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=19A, \, g=43B}$}\\ \begin{tabular}{|cc|cccccc|}\hline $P$&$Q$&817A&817B&817C&817D&817E&817F\\\hline $3$&$({x + {11}},17) $&$ $&$ $&$ f_?g_?$&$ $&$ $&$ $\\\hline $3$&$({x},2) $&$ g$&$ g$&$ f_?$&$ g_?$&$ $&$ g_?$\\\hline $3$&$({x + {4}},7) $&$ $&$ $&$ f_?$&$ $&$ $&$ $\\\hline $3$&$({x + {70}},79) $&$ $&$ $&$ f_?$&$ $&$ g$&$ $\\\hline $43$&$({x + {11}},17) $&$ $&$ $&$ g_?$&$ $&$ $&$ f$\\\hline $43$&$({x},2) $&$ g$&$ g$&$ $&$ g_?$&$ $&$ fg_?$\\\hline $43$&$({x + {4}},7) $&$ $&$ $&$ $&$ $&$ $&$ f$\\\hline $43$&$({x + {70}},79) $&$ $&$ $&$ $&$ $&$ g$&$ f$\\\hline $5$&$({x + {11}},17) $&$ f$&$ $&$ g_?$&$ $&$ $&$ $\\\hline $5$&$({x},2) $&$ fg$&$ g$&$ $&$ g_?$&$ $&$ g_?$\\\hline $5$&$({x + {4}},7) $&$ f$&$ $&$ $&$ $&$ $&$ $\\\hline $5$&$({x + {70}},79) $&$ f$&$ $&$ $&$ $&$ g$&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=23A, \, g=37A}$}\\ \begin{tabular}{|cc|cccccccc|}\hline $P$&$Q$&851A&851B&851C&851D&851E&851F&851G&851H\\\hline $({x + {8}},11) $&$13$&$ $&$ $&$ $&$ $&$ $&$ g$&$ $&$ $\\\hline $({x + {8}},11) $&$2$&$ g$&$ $&$ $&$ g$&$ g_?$&$ $&$ $&$ g$\\\hline $({x^{2} + x + 1},2) $&$11$&$ $&$ $&$ $&$ $&$ g$&$ f_?$&$ f_?$&$ $\\\hline $({x^{2} + x + 1},2) $&$13$&$ $&$ $&$ $&$ $&$ $&$ f_?g$&$ f_?$&$ $\\\hline $({x + {19}},31) $&$11$&$ $&$ $&$ $&$ f$&$ g$&$ $&$ $&$ $\\\hline $({x + {19}},31) $&$13$&$ $&$ $&$ $&$ f$&$ $&$ g$&$ $&$ $\\\hline $({x + {19}},31) $&$2$&$ g$&$ $&$ $&$ fg$&$ g_?$&$ $&$ $&$ g$\\\hline $({x + {360}},379) $&$11$&$ $&$ $&$ $&$ $&$ fg$&$ $&$ $&$ $\\\hline $({x + {360}},379) $&$13$&$ $&$ $&$ $&$ $&$ f$&$ g$&$ $&$ $\\\hline $({x + {360}},379) $&$2$&$ g$&$ $&$ $&$ g$&$ fg_?$&$ $&$ $&$ g$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=23A, \, g=37B}$}\\ \begin{tabular}{|cc|cccccccc|}\hline $P$&$Q$&851A&851B&851C&851D&851E&851F&851G&851H\\\hline $({x + {8}},11) $&$2$&$ g$&$ $&$ $&$ g$&$ g_?$&$ $&$ $&$ g$\\\hline $({x + {8}},11) $&$3$&$ $&$ g_?$&$ $&$ $&$ $&$ $&$ g$&$ $\\\hline $({x + {8}},11) $&$5$&$ g$&$ $&$ $&$ $&$ $&$ $&$ $&$ $\\\hline $({x^{2} + x + 1},2) $&$3$&$ $&$ g_?$&$ $&$ $&$ $&$ f_?$&$ f_?g$&$ $\\\hline $({x^{2} + x + 1},2) $&$5$&$ g$&$ $&$ $&$ $&$ $&$ f_?$&$ f_?$&$ $\\\hline $({x + {19}},31) $&$2$&$ g$&$ $&$ $&$ fg$&$ g_?$&$ $&$ $&$ g$\\\hline $({x + {19}},31) $&$3$&$ $&$ g_?$&$ $&$ f$&$ $&$ $&$ g$&$ $\\\hline $({x + {19}},31) $&$5$&$ g$&$ $&$ $&$ f$&$ $&$ $&$ $&$ $\\\hline $({x + {360}},379) $&$2$&$ g$&$ $&$ $&$ g$&$ fg_?$&$ $&$ $&$ g$\\\hline $({x + {360}},379) $&$3$&$ $&$ g_?$&$ $&$ $&$ f$&$ $&$ g$&$ $\\\hline $({x + {360}},379) $&$5$&$ g$&$ $&$ $&$ $&$ f$&$ $&$ $&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=79A}$}\\ \begin{tabular}{|cc|cccccccc|}\hline $P$&$Q$&869A&869B&869C&869D&869E&869F&869G&869H\\\hline $2$&$5$&$ $&$ $&$ f$&$ $&$ g_?$&$ $&$ $&$ f_?$\\\hline $2$&$7$&$ $&$ $&$ f$&$ $&$ $&$ $&$ g$&$ f_?$\\\hline $3$&$2$&$ fg$&$ $&$ $&$ g$&$ $&$ f$&$ g_?$&$ g_?$\\\hline $3$&$5$&$ f$&$ $&$ $&$ $&$ g_?$&$ f$&$ $&$ $\\\hline $3$&$7$&$ f$&$ $&$ $&$ $&$ $&$ f$&$ g$&$ $\\\hline $5$&$2$&$ g$&$ $&$ $&$ g$&$ $&$ $&$ fg_?$&$ g_?$\\\hline $5$&$7$&$ $&$ $&$ $&$ $&$ $&$ $&$ fg$&$ $\\\hline $7$&$2$&$ g$&$ $&$ $&$ g$&$ $&$ $&$ fg_?$&$ g_?$\\\hline $7$&$5$&$ $&$ $&$ $&$ $&$ g_?$&$ $&$ f$&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=79B}$}\\ \begin{tabular}{|cc|cccccccc|}\hline $P$&$Q$&869A&869B&869C&869D&869E&869F&869G&869H\\\hline $2$&$({x + {10}},13) $&$ $&$ $&$ f$&$ $&$ $&$ $&$ $&$ f_?$\\\hline $2$&$({x + {1637}},1861) $&$ $&$ $&$ f$&$ $&$ $&$ $&$ $&$ f_?g$\\\hline $2$&$({x + {3680}},5927) $&$ $&$ $&$ f$&$ $&$ $&$ g$&$ $&$ f_?$\\\hline $2$&$({x + {55}},61) $&$ $&$ $&$ f$&$ $&$ $&$ $&$ $&$ f_?g$\\\hline $3$&$({x + {10}},13) $&$ f$&$ $&$ $&$ $&$ $&$ f$&$ $&$ $\\\hline $3$&$({x + {1637}},1861) $&$ f$&$ $&$ $&$ $&$ $&$ f$&$ $&$ g$\\\hline $3$&$({x + 1},2) $&$ fg$&$ $&$ $&$ g$&$ $&$ f$&$ g_?$&$ g_?$\\\hline $3$&$({x + {3680}},5927) $&$ f$&$ $&$ $&$ $&$ $&$ fg$&$ $&$ $\\\hline $3$&$({x + {55}},61) $&$ f$&$ $&$ $&$ $&$ $&$ f$&$ $&$ g$\\\hline $5$&$({x + {10}},13) $&$ $&$ $&$ $&$ $&$ $&$ $&$ f$&$ $\\\hline $5$&$({x + {1637}},1861) $&$ $&$ $&$ $&$ $&$ $&$ $&$ f$&$ g$\\\hline $5$&$({x + 1},2) $&$ g$&$ $&$ $&$ g$&$ $&$ $&$ fg_?$&$ g_?$\\\hline $5$&$({x + {3680}},5927) $&$ $&$ $&$ $&$ $&$ $&$ g$&$ f$&$ $\\\hline $5$&$({x + {55}},61) $&$ $&$ $&$ $&$ $&$ $&$ $&$ f$&$ g$\\\hline $7$&$({x + {10}},13) $&$ $&$ $&$ $&$ $&$ $&$ $&$ f$&$ $\\\hline $7$&$({x + {1637}},1861) $&$ $&$ $&$ $&$ $&$ $&$ $&$ f$&$ g$\\\hline $7$&$({x + 1},2) $&$ g$&$ $&$ $&$ g$&$ $&$ $&$ fg_?$&$ g_?$\\\hline $7$&$({x + {3680}},5927) $&$ $&$ $&$ $&$ $&$ $&$ g$&$ f$&$ $\\\hline $7$&$({x + {55}},61) $&$ $&$ $&$ $&$ $&$ $&$ $&$ f$&$ g$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=19A, \, g=47A}$}\\ \begin{tabular}{|cc|cccc|}\hline $P$&$Q$&893A&893B&893C&893D\\\hline $17$&$({x + {304}},1373) $&$ g$&$ $&$ $&$ f$\\\hline $17$&$({x + {37}},139) $&$ $&$ $&$ $&$ fg$\\\hline $17$&$({x^{4} + x^{3} + x^{2} + x + 1},2) $&$ $&$ g_?$&$ g$&$ f$\\\hline $17$&$({x + {20}},23) $&$ $&$ $&$ $&$ f$\\\hline $17$&$({x + 1},3) $&$ $&$ $&$ $&$ fg$\\\hline $17$&$({x + {2}},7) $&$ g_?$&$ $&$ $&$ f$\\\hline $3$&$({x + {304}},1373) $&$ g$&$ f$&$ $&$ $\\\hline $3$&$({x + {37}},139) $&$ $&$ f$&$ $&$ g$\\\hline $3$&$({x^{4} + x^{3} + x^{2} + x + 1},2) $&$ $&$ fg_?$&$ g$&$ $\\\hline $3$&$({x + {20}},23) $&$ $&$ f$&$ $&$ $\\\hline $3$&$({x + {2}},7) $&$ g_?$&$ f$&$ $&$ $\\\hline $5$&$({x + {304}},1373) $&$ g$&$ f$&$ $&$ $\\\hline $5$&$({x + {37}},139) $&$ $&$ f$&$ $&$ g$\\\hline $5$&$({x^{4} + x^{3} + x^{2} + x + 1},2) $&$ $&$ fg_?$&$ g$&$ $\\\hline $5$&$({x + {20}},23) $&$ $&$ f$&$ $&$ $\\\hline $5$&$({x + 1},3) $&$ $&$ f$&$ $&$ g$\\\hline $5$&$({x + {2}},7) $&$ g_?$&$ f$&$ $&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=29A, \, g=31A}$}\\ \begin{tabular}{|cc|cccccc|}\hline $P$&$Q$&899A&899B&899C&899D&899E&899F\\\hline $({x + {52}},113) $&$({x^{2} + x + 1},2) $&$ $&$ $&$ g$&$ $&$ g_?$&$ f$\\\hline $({x + {52}},113) $&$({x + {12}},31) $&$ $&$ $&$ $&$ $&$ $&$ fg$\\\hline $({x + {52}},113) $&$({x + {2}},5) $&$ $&$ $&$ $&$ g$&$ $&$ f$\\\hline $({x + {52}},113) $&$({x + {43}},61) $&$ $&$ $&$ $&$ g$&$ $&$ f$\\\hline $({x + {41}},47) $&$({x^{2} + x + 1},2) $&$ $&$ $&$ g$&$ $&$ fg_?$&$ $\\\hline $({x + {41}},47) $&$({x + {12}},31) $&$ $&$ $&$ $&$ $&$ f$&$ g$\\\hline $({x + {41}},47) $&$({x + {2}},5) $&$ $&$ $&$ $&$ g$&$ f$&$ $\\\hline $({x + {41}},47) $&$({x + {43}},61) $&$ $&$ $&$ $&$ g$&$ f$&$ $\\\hline $({x^{2} + {2}x + {4}},5) $&$({x^{2} + x + 1},2) $&$ $&$ $&$ g$&$ $&$ fg_?$&$ $\\\hline $({x^{2} + {2}x + {4}},5) $&$({x + {12}},31) $&$ $&$ $&$ $&$ $&$ f$&$ g$\\\hline $({x^{2} + {2}x + {4}},5) $&$({x + {43}},61) $&$ $&$ $&$ $&$ g$&$ f$&$ $\\\hline $({x + {4}},7) $&$({x^{2} + x + 1},2) $&$ $&$ $&$ g$&$ $&$ g_?$&$ $\\\hline $({x + {4}},7) $&$({x + {12}},31) $&$ $&$ $&$ $&$ $&$ $&$ g$\\\hline $({x + {4}},7) $&$({x + {2}},5) $&$ $&$ $&$ $&$ g$&$ $&$ $\\\hline $({x + {4}},7) $&$({x + {43}},61) $&$ $&$ $&$ $&$ g$&$ $&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=17A, \, g=53A}$}\\ \begin{tabular}{|cc|cccccccccc|}\hline $P$&$Q$&901A&901B&901C&901D&901E&901F&901G&901H&901I&901J\\\hline $2$&$3$&$ f$&$ $&$ fg$&$ $&$ g$&$ $&$ f_?$&$ $&$ f_?$&$ f_?$\\\hline $2$&$5$&$ fg$&$ $&$ f$&$ $&$ $&$ $&$ f_?$&$ $&$ f_?$&$ f_?$\\\hline $2$&$7$&$ f$&$ $&$ f$&$ $&$ $&$ $&$ f_?$&$ $&$ f_?$&$ f_?g$\\\hline $3$&$5$&$ g$&$ $&$ $&$ $&$ $&$ f$&$ $&$ $&$ $&$ f_?$\\\hline $3$&$7$&$ $&$ $&$ $&$ $&$ $&$ f$&$ $&$ $&$ $&$ f_?g$\\\hline $5$&$3$&$ $&$ $&$ g$&$ $&$ fg$&$ $&$ $&$ $&$ $&$ $\\\hline $5$&$7$&$ $&$ $&$ $&$ $&$ f$&$ $&$ $&$ $&$ $&$ g$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=17A, \, g=53B}$}\\ \begin{tabular}{|cc|cccccccccc|}\hline $P$&$Q$&901A&901B&901C&901D&901E&901F&901G&901H&901I&901J\\\hline $2$&$({x + {47}},113) $&$ f$&$ $&$ f$&$ $&$ $&$ $&$ f_?g$&$ $&$ f_?$&$ f_?$\\\hline $2$&$({x + {10}},13) $&$ f$&$ $&$ f$&$ $&$ $&$ $&$ f_?$&$ $&$ f_?$&$ f_?$\\\hline $2$&$({x + {2078}},4139) $&$ f$&$ $&$ f$&$ $&$ $&$ $&$ f_?$&$ $&$ f_?g$&$ f_?$\\\hline $2$&$({x + {3}},5) $&$ f$&$ $&$ f$&$ $&$ $&$ g$&$ f_?$&$ $&$ f_?$&$ f_?$\\\hline $3$&$({x + {47}},113) $&$ $&$ $&$ $&$ $&$ $&$ f$&$ g$&$ $&$ $&$ f_?$\\\hline $3$&$({x + {10}},13) $&$ $&$ $&$ $&$ $&$ $&$ f$&$ $&$ $&$ $&$ f_?$\\\hline $3$&$({x + {2078}},4139) $&$ $&$ $&$ $&$ $&$ $&$ f$&$ $&$ $&$ g$&$ f_?$\\\hline $3$&$({x + {3}},5) $&$ $&$ $&$ $&$ $&$ $&$ fg$&$ $&$ $&$ $&$ f_?$\\\hline $5$&$({x + {47}},113) $&$ $&$ $&$ $&$ $&$ f$&$ $&$ g$&$ $&$ $&$ $\\\hline $5$&$({x + {10}},13) $&$ $&$ $&$ $&$ $&$ f$&$ $&$ $&$ $&$ $&$ $\\\hline $5$&$({x + {2078}},4139) $&$ $&$ $&$ $&$ $&$ f$&$ $&$ $&$ $&$ g$&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=83A}$}\\ \begin{tabular}{|cc|ccccccc|}\hline $P$&$Q$&913A&913B&913C&913D&913E&913F&913G\\\hline $13$&$3$&$ $&$ $&$ $&$ g$&$ fg$&$ $&$ $\\\hline $13$&$5$&$ $&$ $&$ $&$ g$&$ f$&$ $&$ $\\\hline $2$&$3$&$ $&$ f$&$ $&$ fg$&$ g$&$ $&$ $\\\hline $2$&$5$&$ $&$ f$&$ $&$ fg$&$ $&$ $&$ $\\\hline $3$&$5$&$ $&$ $&$ $&$ g$&$ f$&$ $&$ f_?$\\\hline $5$&$3$&$ $&$ $&$ $&$ g$&$ g$&$ $&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=83B}$}\\ \begin{tabular}{|cc|ccccccc|}\hline $P$&$Q$&913A&913B&913C&913D&913E&913F&913G\\\hline $13$&$({x + {5727}},10007) $&$ $&$ $&$ g$&$ $&$ f$&$ $&$ $\\\hline $13$&$({x + {31}},197) $&$ $&$ $&$ $&$ $&$ f$&$ $&$ g$\\\hline $13$&$({x + {5}},37) $&$ $&$ $&$ $&$ $&$ f$&$ g$&$ $\\\hline $13$&$({x + {69}},379) $&$ $&$ $&$ $&$ $&$ f$&$ $&$ g$\\\hline $13$&$({x + {38}},41) $&$ $&$ $&$ $&$ $&$ f$&$ $&$ $\\\hline $13$&$({x + 1},5) $&$ g$&$ $&$ $&$ $&$ f$&$ $&$ $\\\hline $2$&$({x + {5727}},10007) $&$ $&$ f$&$ g$&$ f$&$ $&$ $&$ $\\\hline $2$&$({x + {31}},197) $&$ $&$ f$&$ $&$ f$&$ $&$ $&$ g$\\\hline $2$&$({x + {5}},37) $&$ $&$ f$&$ $&$ f$&$ $&$ g$&$ $\\\hline $2$&$({x + {69}},379) $&$ $&$ f$&$ $&$ f$&$ $&$ $&$ g$\\\hline $2$&$({x + {38}},41) $&$ $&$ f$&$ $&$ f$&$ $&$ $&$ $\\\hline $2$&$({x + 1},5) $&$ g$&$ f$&$ $&$ f$&$ $&$ $&$ $\\\hline $3$&$({x + {5727}},10007) $&$ $&$ $&$ g$&$ $&$ f$&$ $&$ f_?$\\\hline $3$&$({x + {31}},197) $&$ $&$ $&$ $&$ $&$ f$&$ $&$ f_?g$\\\hline $3$&$({x + {5}},37) $&$ $&$ $&$ $&$ $&$ f$&$ g$&$ f_?$\\\hline $3$&$({x + {69}},379) $&$ $&$ $&$ $&$ $&$ f$&$ $&$ f_?g$\\\hline $3$&$({x + {38}},41) $&$ $&$ $&$ $&$ $&$ f$&$ $&$ f_?$\\\hline $3$&$({x + 1},5) $&$ g$&$ $&$ $&$ $&$ f$&$ $&$ f_?$\\\hline $5$&$({x + {5727}},10007) $&$ $&$ $&$ g$&$ $&$ $&$ $&$ $\\\hline $5$&$({x + {31}},197) $&$ $&$ $&$ $&$ $&$ $&$ $&$ g$\\\hline $5$&$({x + {5}},37) $&$ $&$ $&$ $&$ $&$ $&$ g$&$ $\\\hline $5$&$({x + {69}},379) $&$ $&$ $&$ $&$ $&$ $&$ $&$ g$\\\hline $5$&$({x + {38}},41) $&$ $&$ $&$ $&$ $&$ $&$ $&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=23A, \, g=41A}$} {\small (char 2 primes for $g$ omitted}\\ \begin{tabular}{|cc|ccccc|}\hline $P$&$Q$&943A&943B&943C&943D&943E\\\hline $({x + {8}},11) $&$({x + {7}},13) $&$ $&$ $&$ g$&$ $&$ $\\\hline $({x + {8}},11) $&$({x + {10}},37) $&$ $&$ $&$ g$&$ $&$ $\\\hline $({x + {8}},11) $&$({x + {2}},5) $&$ $&$ $&$ $&$ $&$ $\\\hline $({x + {8}},11) $&$({x + {31}},67) $&$ $&$ $&$ $&$ $&$ g$\\\hline $({x + {124}},151) $&$({x + {7}},13) $&$ $&$ $&$ g$&$ $&$ f$\\\hline $({x + {124}},151) $&$({x + {10}},37) $&$ $&$ $&$ g$&$ $&$ f$\\\hline $({x + {124}},151) $&$({x + {2}},5) $&$ $&$ $&$ $&$ $&$ f$\\\hline $({x + {124}},151) $&$({x + {31}},67) $&$ $&$ $&$ $&$ $&$ fg$\\\hline $({x + {13}},31) $&$({x + {7}},13) $&$ $&$ $&$ g$&$ f_?$&$ $\\\hline $({x + {13}},31) $&$({x + {10}},37) $&$ $&$ $&$ g$&$ f_?$&$ $\\\hline $({x + {13}},31) $&$({x + {2}},5) $&$ $&$ $&$ $&$ f_?$&$ $\\\hline $({x + {13}},31) $&$({x + {31}},67) $&$ $&$ $&$ $&$ f_?$&$ g$\\\hline $({x + {34}},59) $&$({x + {7}},13) $&$ $&$ $&$ g$&$ f$&$ $\\\hline $({x + {34}},59) $&$({x + {10}},37) $&$ $&$ $&$ g$&$ f$&$ $\\\hline $({x + {34}},59) $&$({x + {2}},5) $&$ $&$ $&$ $&$ f$&$ $\\\hline $({x + {34}},59) $&$({x + {31}},67) $&$ $&$ $&$ $&$ f$&$ g$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=89A}$}\\ \begin{tabular}{|cc|cccccc|}\hline $P$&$Q$&979A&979B&979C&979D&979E&979F\\\hline $3$&$2$&$ f$&$ g_?$&$ $&$ $&$ f_?g_?$&$ $\\\hline $3$&$5$&$ f$&$ g$&$ $&$ $&$ f_?$&$ $\\\hline $3$&$7$&$ f$&$ $&$ $&$ $&$ f_?g$&$ $\\\hline $5$&$2$&$ $&$ g_?$&$ f$&$ $&$ fg_?$&$ $\\\hline $5$&$7$&$ $&$ $&$ f$&$ $&$ fg$&$ $\\\hline $7$&$2$&$ $&$ g_?$&$ $&$ $&$ fg_?$&$ $\\\hline $7$&$5$&$ $&$ g$&$ $&$ $&$ f$&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=89B}$}\\ \begin{tabular}{|cc|cccccc|}\hline $P$&$Q$&979A&979B&979C&979D&979E&979F\\\hline $3$&$2$&$ fg$&$ g_?$&$ $&$ g_?$&$ f_?g_?$&$ $\\\hline $5$&$2$&$ g$&$ g_?$&$ f$&$ g_?$&$ fg_?$&$ $\\\hline $7$&$2$&$ g$&$ g_?$&$ $&$ g_?$&$ fg_?$&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=89C}$} {\small (char 2 primes for g omitted)}\\ \begin{tabular}{|cc|cccccc|}\hline $P$&$Q$&979A&979B&979C&979D&979E&979F\\\hline $3$&$({x + {8}},11) $&$ f$&$ $&$ $&$ $&$ f_?$&$ $\\\hline $3$&$({x + {35}},113) $&$ f$&$ $&$ $&$ g$&$ f_?$&$ $\\\hline $3$&$({x + {161}},179) $&$ f$&$ $&$ $&$ g$&$ f_?$&$ $\\\hline $3$&$({x + {177}},607) $&$ f$&$ $&$ g$&$ $&$ f_?$&$ $\\\hline $5$&$({x + {8}},11) $&$ $&$ $&$ f$&$ $&$ f$&$ $\\\hline $5$&$({x + {35}},113) $&$ $&$ $&$ f$&$ g$&$ f$&$ $\\\hline $5$&$({x + {161}},179) $&$ $&$ $&$ f$&$ g$&$ f$&$ $\\\hline $5$&$({x + {177}},607) $&$ $&$ $&$ fg$&$ $&$ f$&$ $\\\hline $7$&$({x + {8}},11) $&$ $&$ $&$ $&$ $&$ f$&$ $\\\hline $7$&$({x + {35}},113) $&$ $&$ $&$ $&$ g$&$ f$&$ $\\\hline $7$&$({x + {161}},179) $&$ $&$ $&$ $&$ g$&$ f$&$ $\\\hline $7$&$({x + {177}},607) $&$ $&$ $&$ g$&$ $&$ f$&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=23A, \, g=43A}$}\\ \begin{tabular}{|cc|cccccc|}\hline $P$&$Q$&989A&989B&989C&989D&989E&989F\\\hline $({x + {4}},11) $&$23$&$ $&$ $&$ $&$ f$&$ g$&$ f$\\\hline $({x + {4}},11) $&$5$&$ $&$ $&$ $&$ fg$&$ $&$ f$\\\hline $({x + {8}},11) $&$23$&$ $&$ $&$ $&$ f$&$ g$&$ $\\\hline $({x + {8}},11) $&$5$&$ $&$ $&$ $&$ fg$&$ $&$ $\\\hline $({x^{2} + x + 1},2) $&$23$&$ $&$ f_?$&$ f_?$&$ f_?$&$ f_?g$&$ $\\\hline $({x^{2} + x + 1},2) $&$5$&$ $&$ f_?$&$ f_?$&$ f_?g$&$ f_?$&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=23A, \, g=43B}$}\\ \begin{tabular}{|cc|cccccc|}\hline $P$&$Q$&989A&989B&989C&989D&989E&989F\\\hline $({x + {4}},11) $&$({x + {142}},593) $&$ $&$ $&$ g$&$ f$&$ $&$ f$\\\hline $({x + {4}},11) $&$({x + {4}},7) $&$ $&$ $&$ $&$ f$&$ $&$ f$\\\hline $({x + {4}},11) $&$({x + {59}},71) $&$ $&$ $&$ $&$ f$&$ $&$ fg$\\\hline $({x + {8}},11) $&$({x + {142}},593) $&$ $&$ $&$ g$&$ f$&$ $&$ $\\\hline $({x + {8}},11) $&$({x + {4}},7) $&$ $&$ $&$ $&$ f$&$ $&$ $\\\hline $({x + {8}},11) $&$({x + {59}},71) $&$ $&$ $&$ $&$ f$&$ $&$ g$\\\hline $({x^{2} + x + 1},2) $&$({x + {142}},593) $&$ $&$ f_?$&$ f_?g$&$ f_?$&$ f_?$&$ $\\\hline $({x^{2} + x + 1},2) $&$({x + {4}},7) $&$ $&$ f_?$&$ f_?$&$ f_?$&$ f_?$&$ $\\\hline $({x^{2} + x + 1},2) $&$({x + {59}},71) $&$ $&$ f_?$&$ f_?$&$ f_?$&$ f_?$&$ g$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=17A, \, g=59A}$} {\small (char 2 primes for g omitted)}\\ \begin{tabular}{|cc|cccccccccc|}\hline $P$&$Q$&1003A&1003B&1003C&1003D&1003E&1003F&1003G&1003H&1003I&1003J\\\hline $2$&$({x + {3}},19) $&$ $&$ $&$ $&$ f$&$ $&$ f_?$&$ g$&$ $&$ f_?$&$ $\\\hline $2$&$({x + {26}},29) $&$ $&$ $&$ $&$ f$&$ $&$ f_?$&$ $&$ $&$ f_?$&$ $\\\hline $2$&$({x + {22}},97) $&$ $&$ $&$ $&$ f$&$ $&$ f_?$&$ g$&$ $&$ f_?$&$ $\\\hline $2$&$({x + {61609}},97001) $&$ $&$ $&$ $&$ f$&$ $&$ f_?g$&$ $&$ $&$ f_?$&$ $\\\hline $3$&$({x + {3}},19) $&$ f$&$ $&$ $&$ $&$ $&$ $&$ f_?g$&$ $&$ $&$ f$\\\hline $3$&$({x + {26}},29) $&$ f$&$ $&$ $&$ $&$ $&$ $&$ f_?$&$ $&$ $&$ f$\\\hline $3$&$({x + {22}},97) $&$ f$&$ $&$ $&$ $&$ $&$ $&$ f_?g$&$ $&$ $&$ f$\\\hline $3$&$({x + {61609}},97001) $&$ f$&$ $&$ $&$ $&$ $&$ g$&$ f_?$&$ $&$ $&$ f$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=19A, \, g=53A}$}\\ \begin{tabular}{|cc|ccccc|}\hline $P$&$Q$&1007A&1007B&1007C&1007D&1007E\\\hline $11$&$3$&$ g$&$ $&$ $&$ $&$ f$\\\hline $11$&$5$&$ $&$ $&$ g$&$ $&$ fg_?$\\\hline $2$&$3$&$ fg$&$ $&$ $&$ f_?$&$ $\\\hline $2$&$5$&$ f$&$ $&$ g$&$ f_?$&$ g_?$\\\hline $3$&$5$&$ $&$ $&$ g$&$ $&$ fg_?$\\\hline $7$&$3$&$ g$&$ f$&$ $&$ $&$ $\\\hline $7$&$5$&$ $&$ f$&$ g$&$ $&$ g_?$\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=19A, \, g=53B}$}\\ \begin{tabular}{|cc|ccccc|}\hline $P$&$Q$&1007A&1007B&1007C&1007D&1007E\\\hline $11$&$({x + {10}},13) $&$ $&$ $&$ $&$ $&$ f$\\\hline $11$&$({x + {24}},13177) $&$ $&$ $&$ $&$ g$&$ f$\\\hline $11$&$({x + {315}},331) $&$ $&$ g$&$ $&$ $&$ f$\\\hline $2$&$({x + {10}},13) $&$ f$&$ $&$ $&$ f_?$&$ $\\\hline $2$&$({x + {24}},13177) $&$ f$&$ $&$ $&$ f_?g$&$ $\\\hline $2$&$({x + {315}},331) $&$ f$&$ g$&$ $&$ f_?$&$ $\\\hline $3$&$({x + {10}},13) $&$ $&$ $&$ $&$ $&$ f$\\\hline $3$&$({x + {24}},13177) $&$ $&$ $&$ $&$ g$&$ f$\\\hline $3$&$({x + {315}},331) $&$ $&$ g$&$ $&$ $&$ f$\\\hline $7$&$({x + {10}},13) $&$ $&$ f$&$ $&$ $&$ $\\\hline $7$&$({x + {24}},13177) $&$ $&$ f$&$ $&$ g$&$ $\\\hline $7$&$({x + {315}},331) $&$ $&$ fg$&$ $&$ $&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=17A, \, g=61A}$}\\ \begin{tabular}{|cc|ccccc|}\hline $P$&$Q$&1037A&1037B&1037C&1037D&1037E\\\hline $13$&$11$&$ g$&$ $&$ $&$ f$&$ $\\\hline $13$&$2$&$ $&$ g_?$&$ $&$ fg_?$&$ $\\\hline $13$&$7$&$ $&$ $&$ $&$ fg$&$ $\\\hline $2$&$11$&$ g$&$ f_?$&$ $&$ f_?$&$ f$\\\hline $2$&$7$&$ $&$ f_?$&$ $&$ f_?g$&$ f$\\\hline $3$&$11$&$ g$&$ $&$ f$&$ $&$ $\\\hline $3$&$2$&$ $&$ g_?$&$ f$&$ g_?$&$ $\\\hline $3$&$7$&$ $&$ $&$ f$&$ g$&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=17A, \, g=61B}$}\\ \begin{tabular}{|cc|ccccc|}\hline $P$&$Q$&1037A&1037B&1037C&1037D&1037E\\\hline $13$&$({x + {141}},1259) $&$ $&$ $&$ $&$ f$&$ g$\\\hline $13$&$({x + 1},2) $&$ $&$ g_?$&$ $&$ fg_?$&$ $\\\hline $13$&$({x + {177}},317) $&$ $&$ $&$ g$&$ f$&$ $\\\hline $13$&$({x + {2}},5) $&$ $&$ $&$ $&$ f$&$ $\\\hline $2$&$({x + {141}},1259) $&$ $&$ f_?$&$ $&$ f_?$&$ fg$\\\hline $2$&$({x + {177}},317) $&$ $&$ f_?$&$ g$&$ f_?$&$ f$\\\hline $2$&$({x + {2}},5) $&$ $&$ f_?$&$ $&$ f_?$&$ f$\\\hline $3$&$({x + {141}},1259) $&$ $&$ $&$ f$&$ $&$ g$\\\hline $3$&$({x + 1},2) $&$ $&$ g_?$&$ f$&$ g_?$&$ $\\\hline $3$&$({x + {177}},317) $&$ $&$ $&$ fg$&$ $&$ $\\\hline $3$&$({x + {2}},5) $&$ $&$ $&$ f$&$ $&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=97A}$}\\ \begin{tabular}{|cc|cccccc|}\hline $P$&$Q$&1067A&1067B&1067C&1067D&1067E&1067F\\\hline $13$&$({x + {28}},41) $&$ $&$ $&$ $&$ fg$&$ $&$ $\\\hline $13$&$({x + {58}},71) $&$ $&$ g$&$ $&$ f$&$ $&$ $\\\hline $13$&$({x + {11}},881) $&$ $&$ $&$ $&$ f$&$ g$&$ $\\\hline $3$&$({x + {28}},41) $&$ $&$ $&$ f$&$ g$&$ $&$ $\\\hline $3$&$({x + {58}},71) $&$ $&$ g$&$ f$&$ $&$ $&$ $\\\hline $3$&$({x + {11}},881) $&$ $&$ $&$ f$&$ $&$ g$&$ $\\\hline $5$&$({x + {28}},41) $&$ $&$ $&$ $&$ g$&$ $&$ $\\\hline $5$&$({x + {58}},71) $&$ $&$ g$&$ $&$ $&$ $&$ $\\\hline $5$&$({x + {11}},881) $&$ $&$ $&$ $&$ $&$ g$&$ $\\\hline $7$&$({x + {28}},41) $&$ f$&$ $&$ f$&$ g$&$ $&$ $\\\hline $7$&$({x + {58}},71) $&$ f$&$ g$&$ f$&$ $&$ $&$ $\\\hline $7$&$({x + {11}},881) $&$ f$&$ $&$ f$&$ $&$ g$&$ $\\\hline \end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{f=11A, \, g=97B}$}\\ \begin{tabular}{|cc|cccccc|}\hline $P$&$Q$&1067A&1067B&1067C&1067D&1067E&1067F\\\hline $13$&$({x + {4}},11) $&$ $&$ $&$ g$&$ f$&$ $&$ $\\\hline $13$&$({x + 1},2) $&$ $&$ $&$ $&$ fg_?$&$ g$&$ g_?$\\\hline $13$&$({x + {1040}},3361) $&$ $&$ $&$ $&$ f$&$ $&$ g$\\\hline $13$&$({x + {31}},61) $&$ $&$ $&$ g$&$ f$&$ $&$ $\\\hline $3$&$({x + {4}},11) $&$ $&$ $&$ fg$&$ $&$ $&$ $\\\hline $3$&$({x + 1},2) $&$ $&$ $&$ f$&$ g_?$&$ g$&$ g_?$\\\hline $3$&$({x + {1040}},3361) $&$ $&$ $&$ f$&$ $&$ $&$ g$\\\hline $3$&$({x + {31}},61) $&$ $&$ $&$ fg$&$ $&$ $&$ $\\\hline $5$&$({x + {4}},11) $&$ $&$ $&$ g$&$ $&$ $&$ $\\\hline $5$&$({x + 1},2) $&$ $&$ $&$ $&$ g_?$&$ g$&$ g_?$\\\hline $5$&$({x + {1040}},3361) $&$ $&$ $&$ $&$ $&$ $&$ g$\\\hline $5$&$({x + {31}},61) $&$ $&$ $&$ g$&$ $&$ $&$ $\\\hline $7$&$({x + {4}},11) $&$ f$&$ $&$ fg$&$ $&$ $&$ $\\\hline $7$&$({x + 1},2) $&$ f$&$ $&$ f$&$ g_?$&$ g$&$ g_?$\\\hline $7$&$({x + {1040}},3361) $&$ f$&$ $&$ f$&$ $&$ $&$ g$\\\hline $7$&$({x + {31}},61) $&$ f$&$ $&$ fg$&$ $&$ $&$ $\\\hline \end{tabular}\end{minipage} \newpage \section{Table of Eigenforms} {\Large The characteristic polynomial of $T_2$ on $S_2(\Gamma_0(N))$ has distinct roots for all prime levels $\leq 97$. Thus a conjugacy class of each such eigenform is determined by giving a factor of the characteristic polynomial. The same is not the case for the levels $NM$ considered, but at least some $T_p$ determines each newform.} \vspace{1in} \begin{center} \begin{tabular}{|l|l|}\hline Form&Factor of $T_2$\\\hline 11A& ${x + {2}} $\\ 17A& ${x + 1} $\\ 19A& ${x} $\\ 23A& ${x^{2} + x - 1} $\\ 29A& ${x^{2} + {2}x - 1} $\\ 31A& ${x^{2} - x - 1} $\\ 37A& ${x + {2}} $\\ 37B& ${x} $\\ 41A& ${x^{3} + x^{2} - {5}x - 1} $\\ 43A& ${x + {2}} $\\ 43B& ${x^{2} - {2}} $\\ 47A& ${x^{4} - x^{3} - {5}x^{2} + {5}x - 1} $\\ 53A& ${x + 1} $\\ 53B& ${x^{3} + x^{2} - {3}x - 1} $\\ 59A& ${x^{5} - {9}x^{3} + {2}x^{2} + {16}x - {8}} $\\ 61A& ${x + 1} $\\ 61B& ${x^{3} - x^{2} - {3}x + 1} $\\ 67A& ${x - {2}} $\\ 67B& ${x^{2} + x - 1} $\\ 67C& ${x^{2} + {3}x + 1} $\\ 71A& ${x^{3} - {5}x + {3}} $\\ 71B& ${x^{3} + x^{2} - {4}x - {3}} $\\ 73A& ${x - 1} $\\ 73B& ${x^{2} - x - {3}} $\\ 73C& ${x^{2} + {3}x + 1} $\\ 79A& ${x + 1} $\\ 79B& ${x^{5} - {6}x^{3} + {8}x - 1} $\\ 83A& ${x + 1} $\\ 83B& ${x^{6} - x^{5} - {9}x^{4} + {7}x^{3} + {20}x^{2} - {12}x - {8}} $\\ 89A& ${x + 1} $\\ 89B& ${x - 1} $\\ 89C& ${x^{5} + x^{4} - {10}x^{3} - {10}x^{2} + {21}x + {17}} $\\ 97A& ${x^{3} + {4}x^{2} + {3}x - 1} $\\ 97B& ${x^{4} - {3}x^{3} - x^{2} + {6}x - 1} $\\\hline \end{tabular} \end{center} \newpage {\small \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{143}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 143A& ${x^{4} - {3}x^{3} - x^{2} + {5}x + 1} $\\ 143B& ${x^{6} - {10}x^{4} + {2}x^{3} + {24}x^{2} - {7}x - {12}} $\\ 143C& ${x} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{187}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{3}$\\\hline 187A& ${x - 1} $\\ 187B& ${x^{2} + x - {4}} $\\ 187C& ${x^{2} - {3}} $\\ 187D& ${x^{3} + {3}x^{2} - x - {5}} $\\ 187E& ${x^{4} - x^{3} - {11}x^{2} + {9}x + {20}} $\\ 187F& ${x} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{209}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 209A& ${x^{2} - {2}} $\\ 209B& ${x^{5} - {2}x^{4} - {6}x^{3} + {10}x^{2} + {5}x - {4}} $\\ 209C& ${x^{7} + x^{6} - {14}x^{5} - {10}x^{4} + {59}x^{3} + {27}x^{2} - {66}x - {30}} $\\ 209D& ${x} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{221}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 221A& ${x - 1} $\\ 221B& ${x + 1} $\\ 221C& ${x^{2} - {5}} $\\ 221D& ${x^{2} + x - 1} $\\ 221E& ${x^{3} - {4}x + 1} $\\ 221F& ${x^{6} - x^{5} - {9}x^{4} + {6}x^{3} + {19}x^{2} - {5}x - {3}} $\\ 221G& ${x^{2} + x - {5}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{247}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 247A& ${x^{2} - x - 1} $\\ 247B& ${x^{3} + {3}x^{2} - {3}} $\\ 247C& ${x^{5} - {4}x^{4} + {12}x^{2} - {5}x - {5}} $\\ 247D& ${x^{5} - {9}x^{3} - x^{2} + {19}x + {4}} $\\ 247E& ${x^{4} + {3}x^{3} - {2}x^{2} - {9}x - {4}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{253}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 253A& ${x^{3} - {3}x^{2} + {3}} $\\ 253B& ${x^{3} + x^{2} - {4}x + 1} $\\ 253C& ${x^{5} + {4}x^{4} - {14}x^{2} - {13}x - 1} $\\ 253D& ${x^{6} - {3}x^{5} - {4}x^{4} + {16}x^{3} - {3}x^{2} - {10}x + 1} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{299}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{5}$\\\hline 299A& ${x^{2} + {3}x + 1} $\\ 299B& ${x^{2} - {3}x - {3}} $\\ 299C& ${x^{2} - {2}x - {4}} $\\ 299D& ${x^{2} + x - 1} $\\ 299E& ${x^{10} - {3}x^{9} - {37}x^{8} + {112}x^{7} + {443}x^{6} - {1401}x^{5} - {1817}x^{4} + {6424}x^{3} + {1108}x^{2} - {6140}x - {2372}} $\\ 299F& ${x^{2} - x - {4}} $\\ 299G& ${x^{3} - x^{2} - {7}x - {3}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{319}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 319A& ${x - {2}} $\\ 319B& ${x^{3} - {3}x - 1} $\\ 319C& ${x^{4} + {2}x^{3} - {3}x^{2} - {3}x + {2}} $\\ 319D& ${x^{7} - {3}x^{6} - {4}x^{5} + {15}x^{4} + x^{3} - {14}x^{2} + 1} $\\ 319E& ${x^{8} - {13}x^{6} - x^{5} + {50}x^{4} + {7}x^{3} - {54}x^{2} - {5}x + 1} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{323}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 323A& ${x^{2} + x - {4}} $\\ 323B& ${x^{4} - {6}x^{2} - x + {7}} $\\ 323C& ${x^{5} + {3}x^{4} - {2}x^{3} - {7}x^{2} + {2}x + 1} $\\ 323D& ${x^{6} - {2}x^{5} - {9}x^{4} + {15}x^{3} + {23}x^{2} - {23}x - {21}} $\\ 323E& ${x^{7} - x^{6} - {10}x^{5} + {9}x^{4} + {26}x^{3} - {19}x^{2} - {12}x + {8}} $\\ 323F& ${x} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{341}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{5}$\\\hline 341A& ${x^{2} + {3}x + 1} $\\ 341B& ${x^{4} + x^{3} - {8}x^{2} - {11}x + 1} $\\ 341C& ${x^{8} + {5}x^{7} - {12}x^{6} - {77}x^{5} - {11}x^{4} + {176}x^{3} + {35}x^{2} - {77}x + {9}} $\\ 341D& ${x^{11} - {3}x^{10} - {35}x^{9} + {106}x^{8} + {423}x^{7} - {1261}x^{6} - {2318}x^{5} }$\\&${+ {6533}x^{4} + {5956}x^{3} - {14599}x^{2} - {6045}x + {10618}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{377}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 377A& ${x - 1} $\\ 377B& ${x^{2} - {3}} $\\ 377C& ${x^{5} + x^{4} - {5}x^{3} - {3}x^{2} + {6}x + 1} $\\ 377D& ${x^{7} - {3}x^{6} - {8}x^{5} + {26}x^{4} + {9}x^{3} - {36}x^{2} - {14}x + {3}} $\\ 377E& ${x^{5} + {3}x^{4} - {3}x^{3} - {13}x^{2} - {8}x - 1} $\\ 377F& ${x^{9} - x^{8} - {13}x^{7} + {13}x^{6} + {51}x^{5} - {50}x^{4} - {59}x^{3} + {45}x^{2} + {20}x - {3}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{391}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 391A& ${x^{3} + x^{2} - {4}x - {3}} $\\ 391B& ${x^{3} + x^{2} - {4}x + 1} $\\ 391C& ${x^{9} - {2}x^{8} - {12}x^{7} + {23}x^{6} + {43}x^{5} - {79}x^{4} - {43}x^{3} + {78}x^{2} + {11}x - {21}} $\\ 391D& ${x^{2} + x - 1} $\\ 391E& ${x^{12} - {4}x^{11} - {12}x^{10} + {62}x^{9} + {27}x^{8} - {321}x^{7} + {108}x^{6} + {625}x^{5} - {362}x^{4} - {372}x^{3} + {116}x^{2} + {97}x + {13}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{403}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 403A& ${x^{2} - {3}x + 1} $\\ 403B& ${x^{7} - {2}x^{6} - {9}x^{5} + {17}x^{4} + {20}x^{3} - {37}x^{2} + x + {4}} $\\ 403C& ${x^{8} + x^{7} - {11}x^{6} - {10}x^{5} + {37}x^{4} + {33}x^{3} - {36}x^{2} - {33}x - {4}} $\\ 403D& ${x^{6} + {2}x^{5} - {7}x^{4} - {13}x^{3} + {6}x^{2} + {7}x - {3}} $\\ 403E& ${x^{8} + {5}x^{7} - {30}x^{5} - {24}x^{4} + {54}x^{3} + {54}x^{2} - {28}x - {29}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{407}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 407A& ${x^{4} + x^{3} - {4}x^{2} + 1} $\\ 407B& ${x^{4} - x^{3} - {4}x^{2} + {2}x + {3}} $\\ 407C& ${x^{12} - x^{11} - {18}x^{10} + {18}x^{9} + {111}x^{8} - {104}x^{7} - {274}x^{6} + {212}x^{5} + {255}x^{4} - {129}x^{3} - {78}x^{2} + {4}x + 1} $\\ 407D& ${x^{11} - {2}x^{10} - {16}x^{9} + {32}x^{8} + {89}x^{7} - {179}x^{6} - {201}x^{5} + {407}x^{4} + {168}x^{3} - {333}x^{2} - {51}x + {75}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{437}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{5}$\\\hline 437A& ${x - 1} $\\ 437B& ${x + 1} $\\ 437C& ${x^{2} + {2}x - {4}} $\\ 437D& ${x^{2} + {2}x - 1} $\\ 437E& ${x^{2} - {2}x - {4}} $\\ 437F& ${x^{5} + x^{4} - {7}x^{3} - {5}x^{2} + {10}x + {4}} $\\ 437G& ${x^{8} - {2}x^{7} - {19}x^{6} + {18}x^{5} + {116}x^{4} - {12}x^{3} - {240}x^{2} - {128}x + {16}} $\\ 437H& ${x^{12} + x^{11} - {43}x^{10} - {29}x^{9} + {690}x^{8} + {304}x^{7} - {5116}x^{6} - {1600}x^{5} }$\\&${+ {17904}x^{4} + {4400}x^{3} - {26240}x^{2} - {4736}x + {10368}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{451}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 451A& ${x^{5} + {2}x^{4} - {5}x^{3} - {10}x^{2} + {4}x + {9}} $\\ 451B& ${x^{5} + {2}x^{4} - {3}x^{3} - {4}x^{2} + {2}x + 1} $\\ 451C& ${x^{10} - {4}x^{9} - {6}x^{8} + {38}x^{7} - {7}x^{6} - {105}x^{5} + {74}x^{4} + {77}x^{3} - {74}x^{2} + {8}} $\\ 451D& ${x^{12} - {3}x^{11} - {16}x^{10} + {48}x^{9} + {93}x^{8} - {270}x^{7} - {251}x^{6} + {633}x^{5} + {359}x^{4} }$\\&${- {582}x^{3} - {248}x^{2} + {136}x + {32}} $\\ 451E& ${x} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{473}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{7}$\\\hline 473A& ${x^{2} + {4}x - 1} $\\ 473B& ${x^{2} - {5}} $\\ 473C& ${x^{5} + {9}x^{4} + {23}x^{3} + {9}x^{2} - {30}x - {25}} $\\ 473D& ${x^{5} + {15}x^{4} + {71}x^{3} + {53}x^{2} - {420}x - {799}} $\\ 473E& ${x^{11} - {17}x^{10} + {96}x^{9} - {92}x^{8} - {1043}x^{7} + {3448}x^{6} - {142}x^{5} - {12971}x^{4}}$\\&${ + {13700}x^{3} + {4760}x^{2} - {6848}x + {1024}} $\\ 473F& ${x^{9} - {19}x^{8} + {140}x^{7} - {482}x^{6} + {627}x^{5} + {570}x^{4} - {2324}x^{3} + {1223}x^{2} + {1580}x - {1368}} $\\ 473G& ${x} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{481}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 481A& ${x - 1} $\\ 481B& ${x^{7} + x^{6} - {8}x^{5} - {7}x^{4} + {17}x^{3} + {12}x^{2} - {9}x - {6}} $\\ 481C& ${x^{11} - {3}x^{10} - {14}x^{9} + {45}x^{8} + {64}x^{7} - {237}x^{6} - {99}x^{5} + {529}x^{4} - {7}x^{3} - {460}x^{2} + {67}x + {110}} $\\ 481D& ${x^{11} - {3}x^{10} - {12}x^{9} + {39}x^{8} + {38}x^{7} - {149}x^{6} - {23}x^{5} + {175}x^{4} - {5}x^{3} - {48}x^{2} + {5}x + {2}} $\\ 481E& ${x^{7} + {5}x^{6} + {2}x^{5} - {21}x^{4} - {25}x^{3} + {8}x^{2} + {13}x - {2}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{493}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{3}$\\\hline 493A& ${x + {3}} $\\ 493B& ${x^{2} + x - {4}} $\\ 493C& ${x^{4} - {3}x^{3} - {7}x^{2} + {27}x - {16}} $\\ 493D& ${x^{5} + {2}x^{4} - {5}x^{3} - {10}x^{2} + 1} $\\ 493E& ${x^{6} - {2}x^{5} - {11}x^{4} + {14}x^{3} + {38}x^{2} - {15}x - {26}} $\\ 493F& ${x^{10} + {9}x^{9} + {22}x^{8} - {16}x^{7} - {115}x^{6} - {54}x^{5} + {155}x^{4} + {95}x^{3} - {65}x^{2} - {24}x + {2}} $\\ 493G& ${x^{8} - {6}x^{7} + x^{6} + {44}x^{5} - {42}x^{4} - {85}x^{3} + {80}x^{2} + {42}x - {8}} $\\ 493H& ${x} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{517}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{17}$\\\hline 517A& ${x - {4}} $\\ 517B& ${x + {6}} $\\ 517C& ${x^{2} - {4}x - {28}} $\\ 517D& ${x^{2} - {8}x + {14}} $\\ 517E& ${x^{2} - {4}x + {2}} $\\ 517F& ${x^{2} - {12}} $\\ 517G& ${x^{3} + {6}x^{2} - {18}x - {50}} $\\ 517H& ${x^{3} - {4}x^{2} - {20}x + {66}} $\\ 517I& ${x^{10} + {6}x^{9} - {69}x^{8} - {354}x^{7} + {1881}x^{6} + {7074}x^{5} - {25042}x^{4} }$\\&${- {54922}x^{3} + {148036}x^{2} + {135080}x - {264560}} $\\ 517J& ${x^{10} + {16}x^{9} + {49}x^{8} - {288}x^{7} - {1157}x^{6} + {2224}x^{5} + {5640}x^{4} - {9922}x^{3} - {6252}x^{2} + {17096}x - {7408}} $\\ 517K& ${x} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{527}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 527A& ${x^{5} + {2}x^{4} - {5}x^{3} - {7}x^{2} + {7}x + 1} $\\ 527B& ${x^{2} - x - 1} $\\ 527C& ${x^{7} + x^{6} - {8}x^{5} - {8}x^{4} + {15}x^{3} + {13}x^{2} - {8}x - {5}} $\\ 527D& ${x^{11} + {2}x^{10} - {17}x^{9} - {34}x^{8} + {101}x^{7} + {202}x^{6} - {238}x^{5} - {469}x^{4} + {182}x^{3} + {295}x^{2} - {83}x - {3}} $\\ 527E& ${x^{16} - {3}x^{15} - {22}x^{14} + {70}x^{13} + {179}x^{12} - {631}x^{11} - {642}x^{10} + {2789}x^{9} + {792}x^{8} - {6335}x^{7} }$\\&${+ {903}x^{6} + {6928}x^{5} - {3096}x^{4} - {2631}x^{3} + {2063}x^{2} - {344}x - {11}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{533}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 533A& ${x^{2} - {2}x - 1} $\\ 533B& ${x^{13} - {21}x^{11} + {166}x^{9} + x^{8} - {613}x^{7} - {16}x^{6} + {1074}x^{5} }$\\&${+ {72}x^{4} - {822}x^{3} - {76}x^{2} + {215}x + {27}} $\\ 533C& ${x^{11} + {2}x^{10} - {14}x^{9} - {26}x^{8} + {64}x^{7} + {103}x^{6} }$\\&${- {117}x^{5} - {149}x^{4} + {65}x^{3} + {71}x^{2} + {5}x - 1} $\\ 533D& ${x^{7} + {2}x^{6} - {6}x^{5} - {12}x^{4} + {9}x^{3} + {19}x^{2} - x - {5}} $\\ 533E& ${x^{8} - x^{7} - {10}x^{6} + {8}x^{5} + {31}x^{4} - {22}x^{3} - {28}x^{2} + {22}x - {3}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{551}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{17}$\\\hline 551A& ${x - {2}} $\\ 551B& ${x - {3}} $\\ 551C& ${x + 1} $\\ 551D& ${x^{2} + {2}x - {4}} $\\ 551E& ${x^{3} + {5}x^{2} - {7}x - 1} $\\ 551F& ${x^{16} - {187}x^{14} + {28}x^{13} + {13484}x^{12} - {3248}x^{11} - {473664}x^{10} + {123616}x^{9} + {8434432}x^{8} }$\\&${- {1894272}x^{7} - {70540288}x^{6} + {12555264}x^{5} + {211791872}x^{4} - {65138688}x^{3} }$\\&${- {89800704}x^{2} + {24330240}x + {6635520}} $\\ 551G& ${x^{18} - {7}x^{17} - {179}x^{16} + {1237}x^{15} + {13154}x^{14} - {90768}x^{13} - {504248}x^{12} + {3575872}x^{11} + {10366592}x^{10} }$\\&${ - {81432448}x^{9} - {95461888}x^{8} + {1065127936}x^{7} - {129328640}x^{6} - {7221715968}x^{5} + {8790904832}x^{4} }$\\&${ + {16087502848}x^{3} - {43953332224}x^{2} + {34624585728}x - {8982429696}} $\\ 551H& ${x} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{559}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 559A& ${x^{3} + {3}x^{2} - {3}} $\\ 559B& ${x^{15} - {2}x^{14} - {22}x^{13} + {43}x^{12} + {187}x^{11} - {354}x^{10} - {769}x^{9} + {1395}x^{8} }$\\&${+ {1553}x^{7} - {2684}x^{6} - {1328}x^{5} + {2265}x^{4} + {241}x^{3} - {606}x^{2} + {33}x + {13}} $\\ 559C& ${x^{7} + {2}x^{6} - {6}x^{5} - {9}x^{4} + {11}x^{3} + {10}x^{2} - {5}x - 1} $\\ 559D& ${x^{14} - {7}x^{13} + {3}x^{12} + {78}x^{11} - {145}x^{10} - {243}x^{9} + {758}x^{8} }$\\&${+ {83}x^{7} - {1422}x^{6} + {532}x^{5} + {1004}x^{4} - {525}x^{3} - {224}x^{2} + {82}x + {23}} $\\ 559E& ${x^{4} + x^{3} - {5}x^{2} - {3}x + 1} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{583}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{3}$\\\hline 583A& ${x + 1} $\\ 583B& ${x - 1} $\\ 583C& ${x - {3}} $\\ 583D& ${x^{2} + {2}x - 1} $\\ 583E& ${x^{2} - {3}} $\\ 583F& ${x^{6} - {2}x^{5} - {8}x^{4} + {16}x^{3} + {10}x^{2} - {20}x - 1} $\\ 583G& ${x^{8} + {8}x^{7} + {17}x^{6} - {10}x^{5} - {58}x^{4} - {16}x^{3} + {45}x^{2} + {10}x - 1} $\\ 583H& ${x^{12} - {6}x^{11} - {9}x^{10} + {110}x^{9} - {66}x^{8} - {672}x^{7} + {937}x^{6} + {1492}x^{5} - {3291}x^{4} }$\\&${- {160}x^{3} + {3592}x^{2} - {2256}x + {352}} $\\ 583I& ${x^{10} + x^{9} - {22}x^{8} - {16}x^{7} + {170}x^{6} + {90}x^{5} - {525}x^{4} - {227}x^{3} + {496}x^{2} + {264}x - {16}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{589}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 589A& ${x^{9} - {14}x^{7} + {64}x^{5} + {2}x^{4} - {106}x^{3} - {5}x^{2} + {49}x - {7}} $\\ 589B& ${x^{10} - {13}x^{8} + {53}x^{6} - {4}x^{5} - {77}x^{4} + {13}x^{3} + {38}x^{2} - {10}x - {2}} $\\ 589C& ${x^{3} - x^{2} - {4}x + {2}} $\\ 589D& ${x^{14} - {23}x^{12} + {204}x^{10} - {880}x^{8} + x^{7} + {1913}x^{6} - {12}x^{5} - {1943}x^{4} + {37}x^{3} + {730}x^{2} - {26}x - {18}} $\\ 589E& ${x^{9} + {4}x^{8} - {5}x^{7} - {34}x^{6} - {7}x^{5} + {90}x^{4} + {61}x^{3} - {69}x^{2} - {64}x - {6}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{611}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 611A& ${x - {2}} $\\ 611B& ${x^{14} - {23}x^{12} - x^{11} + {206}x^{10} + {23}x^{9} - {907}x^{8} - {181}x^{7}}$\\&${ + {2027}x^{6} + {615}x^{5} - {2104}x^{4} - {884}x^{3} + {704}x^{2} + {400}x + {32}} $\\ 611C& ${x^{5} - {5}x^{3} - x^{2} + {5}x + 1} $\\ 611D& ${x^{18} + {2}x^{17} - {29}x^{16} - {57}x^{15} + {338}x^{14} + {648}x^{13} - {2033}x^{12} - {3742}x^{11} + {6794}x^{10} + {11595}x^{9} }$\\&${- {12875}x^{8} - {18843}x^{7} + {13831}x^{6} + {14703}x^{5} - {7711}x^{4} - {4190}x^{3} + {1528}x^{2} + {144}x - {48}} $\\ 611E& ${x^{9} + {3}x^{8} - {6}x^{7} - {21}x^{6} + {8}x^{5} + {42}x^{4} + {2}x^{3} - {25}x^{2} - {6}x + 1} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{629}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 629A& ${x - 1} $\\ 629B& ${x + 1} $\\ 629C& ${x - {2}} $\\ 629D& ${x^{5} - {7}x^{3} + {2}x^{2} + {12}x - {7}} $\\ 629E& ${x^{17} + x^{16} - {30}x^{15} - {26}x^{14} + {367}x^{13} + {266}x^{12} - {2349}x^{11} - {1339}x^{10} + {8394}x^{9} }$\\&${+ {3341}x^{8} - {16544}x^{7} - {3504}x^{6} }$\\&${+ {16591}x^{5} + {760}x^{4} - {6981}x^{3} - {59}x^{2} + {1031}x + {48}} $\\ 629F& ${x^{15} - {2}x^{14} - {24}x^{13} + {46}x^{12} + {225}x^{11} - {407}x^{10} - {1050}x^{9} + {1751}x^{8} + {2573}x^{7} }$\\&${- {3822}x^{6} - {3134}x^{5} + {3962}x^{4} + {1409}x^{3} - {1497}x^{2} + {144}x + {17}} $\\ 629G& ${x^{8} - {10}x^{6} + {29}x^{4} + {3}x^{3} - {24}x^{2} - {7}x + {2}} $\\ 629H& ${x} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{649}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{5}$\\\hline 649A& ${x + 1} $\\ 649B& ${x^{2} + x - {9}} $\\ 649C& ${x^{4} + {5}x^{3} + {6}x^{2} - 1} $\\ 649D& ${x^{11} + x^{10} - {31}x^{9} - {14}x^{8} + {351}x^{7} - {24}x^{6} - {1716}x^{5} + {836}x^{4} }$\\&${+ {3140}x^{3} - {2293}x^{2} - {1242}x + {1013}} $\\ 649E& ${x^{17} - {7}x^{16} - {29}x^{15} + {275}x^{14} + {233}x^{13} - {4337}x^{12} + {722}x^{11} + {35220}x^{10} - {20733}x^{9} }$\\&${- {156048}x^{8} + {114636}x^{7} + {366067}x^{6} - {243583}x^{5} - {410049}x^{4} + {137150}x^{3} }$\\&${+ {199305}x^{2} + {8095}x - {14958}} $\\ 649F& ${x^{12} + {5}x^{11} - {24}x^{10} - {152}x^{9} + {28}x^{8} + {1128}x^{7} + {1428}x^{6} - {680}x^{5}}$\\&${ - {1705}x^{4} - {504}x^{3} + {67}x^{2} + {31}x + 1} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{667}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 667A& ${x^{10} + {3}x^{9} - {10}x^{8} - {32}x^{7} + {32}x^{6} + {118}x^{5} - {29}x^{4} - {182}x^{3} - {28}x^{2} + {101}x + {43}} $\\ 667B& ${x^{12} + {3}x^{11} - {13}x^{10} - {41}x^{9} + {54}x^{8} + {188}x^{7} - {77}x^{6} - {342}x^{5} + {13}x^{4} + {215}x^{3} }$\\&${+ {9}x^{2} - {37}x - {5}} $\\ 667C& ${x^{16} - {3}x^{15} - {22}x^{14} + {68}x^{13} + {187}x^{12} - {597}x^{11} - {795}x^{10} + {2592}x^{9} + {1860}x^{8} }$\\&${- {5877}x^{7} - {2496}x^{6} + {6612}x^{5} + {1842}x^{4} - {3011}x^{3} - {505}x^{2} + {336}x + {64}} $\\ 667D& ${x^{13} - {4}x^{12} - {11}x^{11} + {58}x^{10} + {24}x^{9} - {298}x^{8} + {97}x^{7} + {641}x^{6} - {402}x^{5} }$\\&${- {547}x^{4} + {352}x^{3} + {219}x^{2} - {88}x - {40}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{671}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 671A& ${x^{5} + {2}x^{4} - {3}x^{3} - {4}x^{2} + {2}x + 1} $\\ 671B& ${x^{6} - {7}x^{4} + {2}x^{3} + {12}x^{2} - {5}x - {2}} $\\ 671C& ${x^{21} - {37}x^{19} + {2}x^{18} + {582}x^{17} - {65}x^{16} - {5074}x^{15} + {876}x^{14} + {26808}x^{13} - {6340}x^{12}}$\\&${ - {88228}x^{11} + {26710}x^{10} + {179236}x^{9} - {66498}x^{8} - {215174}x^{7} + {94807}x^{6} + {138664}x^{5}}$\\&${ - {70301}x^{4} - {39180}x^{3} + {21784}x^{2} + {3447}x - {2082}} $\\ 671D& ${x^{19} - {5}x^{18} - {18}x^{17} + {122}x^{16} + {78}x^{15} - {1177}x^{14} + {387}x^{13} + {5755}x^{12} - {4673}x^{11} }$\\&${- {15053}x^{10} + {16875}x^{9} + {20141}x^{8} - {28019}x^{7} - {11589}x^{6} + {21077}x^{5} + {1674}x^{4} }$\\&${- {6404}x^{3} + {241}x^{2} + {643}x - {43}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{689}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{3}$\\\hline 689A& ${x + {2}} $\\ 689B& ${x^{3} + x^{2} - {5}x + {2}} $\\ 689C& ${x^{18} - x^{17} - {36}x^{16} + {37}x^{15} + {509}x^{14} - {518}x^{13} - {3591}x^{12} + {3481}x^{11} + {13297}x^{10} }$\\&${- {11814}x^{9} - {24999}x^{8} + {19921}x^{7} + {21688}x^{6} - {16429}x^{5} - {7147}x^{4} + {5528}x^{3} + {440}x^{2} - {464}x + {16}} $\\ 689D& ${x^{2} - x - 1} $\\ 689E& ${x^{2} + x - 1} $\\ 689F& ${x^{18} - {5}x^{17} - {28}x^{16} + {165}x^{15} + {291}x^{14} - {2260}x^{13} - {1207}x^{12} + {16757}x^{11} - {713}x^{10} }$\\&${- {73440}x^{9} + {26157}x^{8} + {194393}x^{7} - {104038}x^{6} - {302555}x^{5} + {191313}x^{4} + {251884}x^{3} }$\\&${- {168800}x^{2} - {85056}x + {55616}} $\\ 689G& ${x^{9} + {3}x^{8} - {10}x^{7} - {33}x^{6} + {24}x^{5} + {105}x^{4} - {7}x^{3} - {116}x^{2} - {16}x + {32}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{697}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{3}$\\\hline 697A& ${x^{3} + {2}x^{2} - {4}x - {6}} $\\ 697B& ${x^{15} + {8}x^{14} + {2}x^{13} - {134}x^{12} - {281}x^{11} + {613}x^{10} + {2238}x^{9} - {281}x^{8} - {6500}x^{7} - {3592}x^{6} + {7246}x^{5} }$\\&${+ {6704}x^{4} - {1852}x^{3} - {2832}x^{2} - {164}x + {220}} $\\ 697C& ${x^{3} - {2}x^{2} - {2}x + {2}} $\\ 697D& ${x^{7} + {2}x^{6} - {12}x^{5} - {18}x^{4} + {35}x^{3} + {21}x^{2} - {14}x + 1} $\\ 697E& ${x^{15} - {4}x^{14} - {24}x^{13} + {106}x^{12} + {213}x^{11} - {1119}x^{10} - {786}x^{9} + {5993}x^{8} + {390}x^{7} - {17050}x^{6}}$\\&${ + {5244}x^{5} + {24068}x^{4} - {13256}x^{3} - {12640}x^{2} + {9184}x - {324}} $\\ 697F& ${x^{10} - {2}x^{9} - {20}x^{8} + {34}x^{7} + {133}x^{6} - {167}x^{5} - {324}x^{4} + {209}x^{3} + {190}x^{2} - {100}x - {2}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{703}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 703A& ${x + {2}} $\\ 703B& ${x^{2} - {2}} $\\ 703C& ${x^{4} - {6}x^{2} + {4}x + {2}} $\\ 703D& ${x^{5} + {3}x^{4} - {3}x^{3} - {14}x^{2} - {7}x + {3}} $\\ 703E& ${x^{11} - {5}x^{10} - {6}x^{9} + {60}x^{8} - {25}x^{7} - {228}x^{6} + {193}x^{5} + {312}x^{4} - {257}x^{3} - {194}x^{2} + {94}x + {54}} $\\ 703F& ${x^{18} - {3}x^{17} - {25}x^{16} + {78}x^{15} + {251}x^{14} - {827}x^{13} - {1294}x^{12} + {4619}x^{11} + {3615}x^{10} - {14679}x^{9} - {5160}x^{8} }$\\&${+ {26821}x^{7} + {2497}x^{6} - {27186}x^{5} + {2136}x^{4} + {13772}x^{3} - {2914}x^{2} - {2636}x + {836}} $\\ 703G& ${x^{4} - {3}x^{3} - {2}x^{2} + {9}x - {4}} $\\ 703H& ${x^{9} + {3}x^{8} - {9}x^{7} - {28}x^{6} + {21}x^{5} + {69}x^{4} - {12}x^{3} - {44}x^{2} - {4}x + {4}} $\\ 703I& ${x} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{713}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 713A& ${x - 1} $\\ 713B& ${x^{2} - x - 1} $\\ 713C& ${x^{5} + {4}x^{4} + x^{3} - {9}x^{2} - {5}x + 1} $\\ 713D& ${x^{15} - x^{14} - {24}x^{13} + {23}x^{12} + {225}x^{11} - {207}x^{10} - {1031}x^{9} + {912}x^{8} + {2343}x^{7} - {1992}x^{6} }$\\&${- {2324}x^{5} + {1872}x^{4} + {675}x^{3} - {428}x^{2} - {69}x + {9}} $\\ 713E& ${x^{18} - {5}x^{17} - {18}x^{16} + {120}x^{15} + {86}x^{14} - {1141}x^{13} + {216}x^{12} + {5545}x^{11} - {3248}x^{10} - {14881}x^{9} + {11254}x^{8}}$\\&${ + {22409}x^{7} - {17505}x^{6} - {18664}x^{5} + {12837}x^{4} + {7970}x^{3} - {3926}x^{2} - {1353}x + {271}} $\\ 713F& ${x^{5} - {7}x^{3} + {11}x - 1} $\\ 713G& ${x^{9} + {5}x^{8} - x^{7} - {38}x^{6} - {43}x^{5} + {52}x^{4} + {102}x^{3} + {31}x^{2} - {11}x - {3}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{731}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{3}$\\\hline 731A& ${x - 1} $\\ 731B& ${x^{2} - x - {4}} $\\ 731C& ${x^{6} + {3}x^{5} - {3}x^{4} - {10}x^{3} + x^{2} + {4}x - 1} $\\ 731D& ${x^{8} + {3}x^{7} - {10}x^{6} - {29}x^{5} + {28}x^{4} + {74}x^{3} - {30}x^{2} - {50}x + {5}} $\\ 731E& ${x^{21} + x^{20} - {48}x^{19} - {41}x^{18} + {964}x^{17} + {674}x^{16} - {10525}x^{15} - {5705}x^{14} + {67848}x^{13} }$\\&${+ {26590}x^{12} - {262265}x^{11} - {68190}x^{10} + {590444}x^{9} + {93377}x^{8} - {719141}x^{7} - {67956}x^{6} + {414111}x^{5} }$\\&${+ {34290}x^{4} - {99217}x^{3} - {11164}x^{2} + {8076}x + {1384}} $\\ 731F& ${x^{19} - {5}x^{18} - {30}x^{17} + {179}x^{16} + {318}x^{15} - {2624}x^{14} - {1061}x^{13} + {20311}x^{12} - {4812}x^{11} }$\\&${- {89702}x^{10} + {50281}x^{9} + {230680}x^{8} - {159654}x^{7} - {344023}x^{6} + {234519}x^{5} + {280066}x^{4} }$\\&${- {154817}x^{3} - {98750}x^{2} + {33639}x + {2568}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{737}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 737A& ${x + {2}} $\\ 737B& ${x^{2} - {2}} $\\ 737C& ${x^{17} - x^{16} - {26}x^{15} + {25}x^{14} + {272}x^{13} - {244}x^{12} - {1472}x^{11} + {1186}x^{10} + {4406}x^{9} - {3042}x^{8} - {7180}x^{7}}$\\&${ + {4055}x^{6} + {5665}x^{5} - {2655}x^{4} - {1418}x^{3} + {810}x^{2} - {76}x - {2}} $\\ 737D& ${x^{12} + {2}x^{11} - {14}x^{10} - {25}x^{9} + {72}x^{8} + {109}x^{7} - {165}x^{6} - {196}x^{5} + {165}x^{4} + {134}x^{3} - {64}x^{2} - {30}x + {6}} $\\ 737E& ${x^{15} - {2}x^{14} - {22}x^{13} + {43}x^{12} + {185}x^{11} - {353}x^{10} - {745}x^{9} + {1391}x^{8} + {1463}x^{7} - {2685}x^{6} - {1277}x^{5} }$\\&${+ {2284}x^{4} + {457}x^{3} - {718}x^{2} - {58}x + {72}} $\\ 737F& ${x^{8} - {2}x^{7} - {8}x^{6} + {15}x^{5} + {12}x^{4} - {19}x^{3} - {7}x^{2} + {6}x + 1} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{767}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{5}$\\\hline 767A& ${x^{3} + x^{2} - {7}x - {9}} $\\ 767B& ${x^{4} + x^{3} - {3}x^{2} - x + 1} $\\ 767C& ${x^{10} + {6}x^{9} - {2}x^{8} - {63}x^{7} - {61}x^{6} + {134}x^{5} + {96}x^{4} - {132}x^{3} + {13}x^{2} + {7}x - 1} $\\ 767D& ${x^{2} + {2}x - 1} $\\ 767E& ${x^{23} - {4}x^{22} - {81}x^{21} + {317}x^{20} + {2801}x^{19} - {10657}x^{18} - {54111}x^{17} + {198312}x^{16} + {643019}x^{15} }$\\&${ - {2238143}x^{14} - {4894174}x^{13} + {15814887}x^{12} + {24187057}x^{11} - {69900276}x^{10} - {77130544}x^{9} }$\\&${+ {187733632}x^{8} + {153123344}x^{7} - {285750528}x^{6} - {173058880}x^{5} + {212348800}x^{4} }$\\&${+ {92806144}x^{3} - {54402560}x^{2} - {20271104}x + {657408}} $\\ 767F& ${x^{17} - {4}x^{16} - {51}x^{15} + {224}x^{14} + {962}x^{13} - {4947}x^{12} - {7716}x^{11} + {54891}x^{10} + {13542}x^{9} }$\\&${- {321428}x^{8}+ {167128}x^{7} + {929632}x^{6} - {981312}x^{5} - {980800}x^{4} + {1623296}x^{3} }$\\&${- {148480}x^{2} - {376320}x + {25600}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{779}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 779A& ${x^{2} - {2}} $\\ 779B& ${x^{8} + {2}x^{7} - {9}x^{6} - {18}x^{5} + {20}x^{4} + {37}x^{3} - {17}x^{2} - {21}x + {4}} $\\ 779C& ${x^{11} - {13}x^{9} + {58}x^{7} + x^{6} - {105}x^{5} - {9}x^{4} + {72}x^{3} + {10}x^{2} - {12}x - {2}} $\\ 779D& ${x^{19} - {31}x^{17} + {403}x^{15} + x^{14} - {2856}x^{13} - {21}x^{12} + {12018}x^{11} + {167}x^{10} - {30705}x^{9} - {609}x^{8} }$\\&${+ {46868}x^{7} + {898}x^{6} - {40530}x^{5} + {48}x^{4} + {17736}x^{3} - {1056}x^{2} - {2912}x + {576}} $\\ 779E& ${x^{21} - x^{20} - {35}x^{19} + {33}x^{18} + {517}x^{17} - {454}x^{16} - {4203}x^{15} + {3401}x^{14} + {20547}x^{13} - {15245}x^{12}}$\\&${ - {61842}x^{11} + {42414}x^{10} + {112133}x^{9} - {73432}x^{8} - {113232}x^{7} + {76256}x^{6} + {51782}x^{5} - {42048}x^{4} }$\\&${- {3816}x^{3} + {8096}x^{2} - {1696}x + {64}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{781}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{7}$\\\hline 781A& ${x + {3}} $\\ 781B& ${x - {3}} $\\ 781C& ${x^{2} - x - {3}} $\\ 781D& ${x^{6} + {6}x^{5} + {6}x^{4} - {20}x^{3} - {41}x^{2} - {22}x - {3}} $\\ 781E& ${x^{15} + {4}x^{14} - {54}x^{13} - {209}x^{12} + {1091}x^{11} + {3742}x^{10} - {11591}x^{9} - {28217}x^{8} + {78036}x^{7} + {82851}x^{6} }$\\&${- {306450}x^{5} + {40124}x^{4} + {479896}x^{3} - {500400}x^{2} + {173536}x - {12352}} $\\ 781F& ${x^{12} - {7}x^{11} - {5}x^{10} + {100}x^{9} - {43}x^{8} - {503}x^{7} + {280}x^{6} + {1099}x^{5} - {371}x^{4} - {964}x^{3} - {36}x^{2} + {128}x - {16}} $\\ 781G& ${x^{20} + {2}x^{19} - {94}x^{18} - {145}x^{17} + {3679}x^{16} + {3686}x^{15} - {77889}x^{14} - {31965}x^{13} + {960848}x^{12} - {170343}x^{11} }$\\&${- {6812398}x^{10} + {4828640}x^{9} + {25056784}x^{8} - {28885904}x^{7} - {37008736}x^{6} + {56238784}x^{5} }$\\&${+ {17695232}x^{4} - {37068288}x^{3} - {4181504}x^{2} + {7863296}x + {1466368}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{793}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 793A& ${x - 1} $\\ 793B& ${x^{16} - {3}x^{15} - {20}x^{14} + {63}x^{13} + {148}x^{12} - {507}x^{11} - {487}x^{10} + {1959}x^{9} + {625}x^{8} - {3706}x^{7} }$\\&${- {35}x^{6} + {3151}x^{5} - {203}x^{4} - {1134}x^{3} + {22}x^{2} + {123}x + {13}} $\\ 793C& ${x^{15} + {8}x^{14} + {8}x^{13} - {89}x^{12} - {231}x^{11} + {242}x^{10} + {1295}x^{9} + {332}x^{8} - {2847}x^{7} - {2275}x^{6} }$\\&${+ {2304}x^{5} + {2831}x^{4} - {194}x^{3} - {792}x^{2} - {54}x + {27}} $\\ 793D& ${x^{9} + {3}x^{8} - {9}x^{7} - {32}x^{6} + {15}x^{5} + {94}x^{4} + {13}x^{3} - {85}x^{2} - {29}x + 1} $\\ 793E& ${x^{4} + x^{3} - {5}x^{2} - x + 1} $\\ 793F& ${x^{16} - {5}x^{15} - {12}x^{14} + {91}x^{13} + {14}x^{12} - {637}x^{11} + {375}x^{10} + {2141}x^{9} - {2071}x^{8} - {3516}x^{7} }$\\&${+ {4367}x^{6} + {2507}x^{5} - {4115}x^{4} - {320}x^{3} + {1504}x^{2} - {249}x - {77}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{799}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{5}$\\\hline 799A& ${x - {4}} $\\ 799B& ${x^{2} + x - 1} $\\ 799C& ${x^{12} + {11}x^{11} + {30}x^{10} - {82}x^{9} - {572}x^{8} - {805}x^{7} + {713}x^{6} + {2431}x^{5} + {656}x^{4} }$\\&${- {1927}x^{3} - {1021}x^{2} + {422}x + {250}} $\\ 799D& ${x^{20} - {13}x^{19} + {14}x^{18} + {482}x^{17} - {1818}x^{16} - {5729}x^{15} + {38323}x^{14} + {9389}x^{13} }$\\&${- {358596}x^{12} + {319657}x^{11} + {1663371}x^{10} - {2674360}x^{9} - {3552042}x^{8} + {8622044}x^{7} + {2202456}x^{6} }$\\&${- {12131764}x^{5} + {1528708}x^{4} + {7557516}x^{3} - {1964948}x^{2} - {1720968}x + {468504}} $\\ 799E& ${x^{8} + {10}x^{7} + {23}x^{6} - {53}x^{5} - {226}x^{4} - {22}x^{3} + {463}x^{2} + {286}x + {7}} $\\ 799F& ${x^{17} - {11}x^{16} + {18}x^{15} + {192}x^{14} - {672}x^{13} - {999}x^{12} + {6135}x^{11} + {503}x^{10} - {24124}x^{9} + {7077}x^{8} }$\\&${+ {44295}x^{7} - {6560}x^{6} - {39544}x^{5} - {9768}x^{4} + {8072}x^{3} + {3900}x^{2} + {420}x - {8}} $\\ 799G& ${x} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{803}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{3}$\\\hline 803A& ${x^{2} - x - {5}} $\\ 803B& ${x^{5} - {2}x^{4} - {9}x^{3} + {8}x^{2} + {25}x + {7}} $\\ 803C& ${x^{19} - {3}x^{18} - {35}x^{17} + {111}x^{16} + {482}x^{15} - {1658}x^{14} - {3304}x^{13} + {12959}x^{12} + {11430}x^{11} }$\\&${- {57301}x^{10} - {15408}x^{9} + {144599}x^{8} - {12824}x^{7} - {200394}x^{6} + {57748}x^{5} + {139435}x^{4} - {49971}x^{3} }$\\&${- {42564}x^{2} + {12386}x + {4307}} $\\ 803D& ${x^{16} - {4}x^{15} - {29}x^{14} + {130}x^{13} + {287}x^{12} - {1615}x^{11} - {856}x^{10} + {9461}x^{9} - {3102}x^{8} - {25236}x^{7} }$\\&${+ {22922}x^{6} + {20598}x^{5} - {34448}x^{4} + {10606}x^{3} + {2476}x^{2} - {1167}x - {20}} $\\ 803E& ${x^{9} + {5}x^{8} - {27}x^{6} - {19}x^{5} + {41}x^{4} + {30}x^{3} - {21}x^{2} - {9}x + 1} $\\ 803F& ${x^{10} + {3}x^{9} - {13}x^{8} - {35}x^{7} + {67}x^{6} + {136}x^{5} - {156}x^{4} - {188}x^{3} + {106}x^{2} + {89}x + {7}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{817}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{7}$\\\hline 817A& ${x - {4}} $\\ 817B& ${x + {4}} $\\ 817C& ${x^{13} + {15}x^{12} + {71}x^{11} - {3}x^{10} - {1037}x^{9} - {2573}x^{8} + {2149}x^{7} + {15828}x^{6} + {12639}x^{5} - {20749}x^{4} }$\\&${- {26976}x^{3} + {7432}x^{2} + {10728}x - {2384}} $\\ 817D& ${x^{15} + {13}x^{14} + {13}x^{13} - {453}x^{12} - {1403}x^{11} + {5879}x^{10} + {24651}x^{9} - {39302}x^{8} - {191153}x^{7} + {177467}x^{6} }$\\&${+ {718900}x^{5} - {651322}x^{4} - {1046764}x^{3} + {1330320}x^{2} - {276448}x - {51552}} $\\ 817E& ${x^{15} - {15}x^{14} + {66}x^{13} + {46}x^{12} - {1072}x^{11} + {2066}x^{10} + {3118}x^{9} - {14751}x^{8} + {11848}x^{7} + {17325}x^{6} }$\\&${- {41887}x^{5} + {35611}x^{4} - {15584}x^{3} + {3624}x^{2} - {408}x + {16}} $\\ 817F& ${x^{18} - {13}x^{17} + {8}x^{16} + {554}x^{15} - {1928}x^{14} - {7628}x^{13} + {46850}x^{12} + {16595}x^{11} - {477198}x^{10} }$\\&${+ {501983}x^{9} + {2190865}x^{8} - {4639631}x^{7} - {3079348}x^{6} + {15233622}x^{5} - {6887244}x^{4} - {16339616}x^{3} }$\\&${+ {18852320}x^{2} - {3841248}x - {1607936}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{851}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{5}$\\\hline 851A& ${x^{2} - x - {10}} $\\ 851B& ${x^{3} - {9}x + {9}} $\\ 851C& ${x^{3} + {4}x^{2} + {3}x - 1} $\\ 851D& ${x^{5} + {3}x^{4} - {5}x^{3} - {5}x^{2} + {3}x + {2}} $\\ 851E& ${x^{20} - {13}x^{19} + {19}x^{18} + {443}x^{17} - {2001}x^{16} - {3445}x^{15} + {36558}x^{14} - {25663}x^{13} }$\\&${- {276167}x^{12} + {502325}x^{11} + {940829}x^{10} - {2798094}x^{9} - {1158810}x^{8} + {7343270}x^{7} - {539281}x^{6} }$\\&${- {9850887}x^{5} + {1677633}x^{4} + {6808852}x^{3} - {224506}x^{2} - {1951231}x - {421276}} $\\ 851F& ${x^{12} + {5}x^{11} - {25}x^{10} - {153}x^{9} + {124}x^{8} + {1495}x^{7} + {688}x^{6} - {5232}x^{5} }$\\&${- {5286}x^{4} + {4299}x^{3} + {5237}x^{2} - {10}x - {484}} $\\ 851G& ${x^{21} - {4}x^{20} - {59}x^{19} + {240}x^{18} + {1389}x^{17} - {5878}x^{16} - {16622}x^{15} + {76555}x^{14} }$\\&${+ {103986}x^{13} - {577015}x^{12} - {276364}x^{11} + {2553842}x^{10} - {280214}x^{9} - {6368404}x^{8} + {3463991}x^{7} }$\\&${+ {7822938}x^{6} - {7350113}x^{5} - {2824907}x^{4} + {5264627}x^{3} - {1375068}x^{2} - {354840}x + {142728}} $\\ 851H& ${x} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{869}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{7}$\\\hline 869A& ${x - 1} $\\ 869B& ${x - {4}} $\\ 869C& ${x + {2}} $\\ 869D& ${x + {5}} $\\ 869E& ${x^{11} + {3}x^{10} - {28}x^{9} - {72}x^{8} + {256}x^{7} + {484}x^{6} - {1056}x^{5} - {1088}x^{4} + {1855}x^{3} + {436}x^{2} - {665}x - {125}} $\\ 869F& ${x^{11} + {7}x^{10} - {14}x^{9} - {174}x^{8} - {64}x^{7} + {1264}x^{6} + {690}x^{5} - {4200}x^{4} - {573}x^{3} + {5980}x^{2} - {2631}x - {277}} $\\ 869G& ${x^{18} - {10}x^{17} - {23}x^{16} + {516}x^{15} - {652}x^{14} - {9304}x^{13} + {25946}x^{12} + {64888}x^{11} - {294601}x^{10} }$\\&${ - {83585}x^{9} + {1368375}x^{8} - {574658}x^{7} - {2942339}x^{6} + {1653448}x^{5} + {3292400}x^{4} }$\\&${- {1009632}x^{3} - {1835808}x^{2} - {376512}x - {4736}} $\\ 869H& ${x^{21} - {10}x^{20} - {51}x^{19} + {802}x^{18} + {34}x^{17} - {24720}x^{16} + {43996}x^{15} + {362766}x^{14} - {1083285}x^{13} }$\\&${- {2442801}x^{12} + {11200143}x^{11} + {4060240}x^{10} - {54269061}x^{9} + {28349170}x^{8} + {107743960}x^{7} }$\\&${- {109829248}x^{6} - {44052576}x^{5} + {59249280}x^{4}}$\\&${ + {15322368}x^{3} - {10312960}x^{2} - {3903488}x - {305152}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{871}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{3}$\\\hline 871A& ${x - {2}} $\\ 871B& ${x^{3} - {6}x + {2}} $\\ 871C& ${x^{8} + {4}x^{7} - x^{6} - {17}x^{5} - {6}x^{4} + {21}x^{3} + {8}x^{2} - {6}x - 1} $\\ 871D& ${x^{20} - {49}x^{18} - {3}x^{17} + {1008}x^{16} + {115}x^{15} - {11336}x^{14} - {1758}x^{13} + {76077}x^{12} + {13646}x^{11} }$\\&${- {312262}x^{10} - {56448}x^{9} + {772280}x^{8} + {118560}x^{7} - {1088640}x^{6} - {107392}x^{5} + {772224}x^{4} }$\\&${ + {36608}x^{3} - {193024}x^{2} - {21504}x + {2048}} $\\ 871E& ${x^{23} - {4}x^{22} - {51}x^{21} + {217}x^{20} + {1062}x^{19} - {4933}x^{18} - {11512}x^{17} + {61028}x^{16} + {67947}x^{15} }$\\&${- {447186}x^{14} - {201188}x^{13} + {1985836}x^{12} + {186230}x^{11} - {5291936}x^{10} + {244520}x^{9} + {8232128}x^{8} }$\\&${- {51264}x^{7} - {7197696}x^{6} - {1144704}x^{5} + {3128064}x^{4} + {1121792}x^{3} - {437248}x^{2} - {288768}x - {40960}} $\\ 871F& ${x^{12} - {2}x^{11} - {13}x^{10} + {23}x^{9} + {60}x^{8} - {91}x^{7} - {120}x^{6} + {154}x^{5} + {107}x^{4} }$\\&${ - {114}x^{3} - {36}x^{2} + {30}x + {2}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{893}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 893A& ${x^{18} - x^{17} - {28}x^{16} + {25}x^{15} + {322}x^{14} - {247}x^{13} - {1971}x^{12} + {1231}x^{11} + {6953}x^{10} - {3283}x^{9} }$\\&${- {14235}x^{8} + {4562}x^{7} + {15962}x^{6} - {2882}x^{5} - {8159}x^{4} + {606}x^{3} + {890}x^{2} - {179}x + {9}} $\\ 893B& ${x^{23} - x^{22} - {38}x^{21} + {37}x^{20} + {622}x^{19} - {586}x^{18} - {5746}x^{17} + {5195}x^{16} + {32986}x^{15} }$\\&${- {28295}x^{14} - {122210}x^{13}+ {97857}x^{12} + {294219}x^{11} - {214815}x^{10} - {452516}x^{9} + {290939}x^{8} }$\\&${+ {425340}x^{7} - {227487}x^{6} - {224027}x^{5} + {88871}x^{4} + {55896}x^{3} - {11568}x^{2} - {4727}x - {315}} $\\ 893C& ${x^{16} + {4}x^{15} - {13}x^{14} - {65}x^{13} + {47}x^{12} + {390}x^{11} + {4}x^{10} - {1115}x^{9} - {320}x^{8} }$\\&${+ {1639}x^{7} + {618}x^{6} - {1250}x^{5} - {487}x^{4} + {456}x^{3} + {179}x^{2} - {62}x - {25}} $\\ 893D& ${x^{12} + x^{11} - {15}x^{10} - {14}x^{9} + {84}x^{8} + {76}x^{7} - {213}x^{6} - {196}x^{5} + {225}x^{4} }$\\&${+ {229}x^{3} - {49}x^{2} - {83}x - {17}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{899}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 899A& ${x - {2}} $\\ 899B& ${x - 1} $\\ 899C& ${x^{11} + {4}x^{10} - {5}x^{9} - {35}x^{8} - {9}x^{7} + {95}x^{6} + {68}x^{5} - {87}x^{4} - {86}x^{3} + {9}x^{2} + {21}x + {3}} $\\ 899D& ${x^{23} - {2}x^{22} - {37}x^{21} + {72}x^{20} + {589}x^{19} - {1114}x^{18} - {5272}x^{17} + {9694}x^{16} + {29077}x^{15} - {52143}x^{14}}$\\&${ - {101680}x^{13} + {179479}x^{12} + {222656}x^{11} - {395841}x^{10} - {286995}x^{9} + {544647}x^{8} + {181121}x^{7}}$\\&${ - {439160}x^{6} - {11748}x^{5} + {181376}x^{4} - {38720}x^{3} - {26048}x^{2} + {11328}x - {1152}} $\\ 899E& ${x^{25} - {43}x^{23} - x^{22} + {803}x^{21} + {41}x^{20} - {8552}x^{19} - {705}x^{18} + {57371}x^{17} + {6615}x^{16} - {252748}x^{15} }$\\&${- {36904}x^{14} + {739489}x^{13} + {124981}x^{12} - {1419906}x^{11} - {250727}x^{10} + {1726030}x^{9} + {273427}x^{8} }$\\&${- {1241767}x^{7}- {126943}x^{6} + {471802}x^{5} + {1736}x^{4} - {77984}x^{3} + {7008}x^{2} + {3968}x - {576}} $\\ 899F& ${x^{10} - {12}x^{8} + {48}x^{6} - {75}x^{4} + {38}x^{2} + {3}x - 1} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{901}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{13}$\\\hline 901A& ${x - {2}} $\\ 901B& ${x - {5}} $\\ 901C& ${x - {6}} $\\ 901D& ${x + {7}} $\\ 901E& ${x - {3}} $\\ 901F& ${x - 1} $\\ 901G& ${x^{13} - {8}x^{12} - {64}x^{11} + {690}x^{10} + {423}x^{9} - {18583}x^{8} + {34111}x^{7} + {150966}x^{6} - {527232}x^{5} }$\\&${+ {49798}x^{4}+ {1393785}x^{3} - {1262290}x^{2} - {94868}x + {275192}} $\\ 901H& ${x^{12} + {16}x^{11} + {49}x^{10} - {340}x^{9} - {1609}x^{8} + {2819}x^{7} + {14122}x^{6} - {17107}x^{5} - {41391}x^{4} }$\\&${+ {49378}x^{3} + {36149}x^{2} - {48120}x + {4637}} $\\ 901I& ${x^{20} - {121}x^{18} - {108}x^{17} + {5622}x^{16} + {9275}x^{15} - {124711}x^{14} - {284725}x^{13} + {1336016}x^{12} }$\\&${+ {3867263}x^{11} - {5865527}x^{10} - {22349231}x^{9} + {4694844}x^{8} + {41540018}x^{7} - {3767109}x^{6} }$\\&${- {29164520}x^{5} + {5810385}x^{4} + {6416556}x^{3} - {1536920}x^{2} - {433536}x + {111424}} $\\ 901J& ${x^{18} + {12}x^{17} - {68}x^{16} - {1388}x^{15} - {934}x^{14} + {59487}x^{13} + {196711}x^{12} - {1059678}x^{11} }$\\&${- {6454793}x^{10} + {2816281}x^{9} + {85456840}x^{8} + {139334462}x^{7} - {357393148}x^{6} - {1366160472}x^{5} }$\\&${- {956290865}x^{4} + {1655736784}x^{3} + {2911246368}x^{2} + {1179800512}x - {88282240}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{913}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 913A& ${x + 1} $\\ 913B& ${x - {2}} $\\ 913C& ${x^{12} - {2}x^{11} - {20}x^{10} + {38}x^{9} + {145}x^{8} - {260}x^{7} - {444}x^{6} + {749}x^{5} + {470}x^{4} }$\\&${ - {778}x^{3} - {7}x^{2} + {169}x - {29}} $\\ 913D& ${x^{16} + {5}x^{15} - {10}x^{14} - {80}x^{13} + {3}x^{12} + {492}x^{11} + {296}x^{10} - {1442}x^{9} - {1323}x^{8} }$\\&${+ {1982}x^{7} + {2237}x^{6}- {988}x^{5} - {1401}x^{4} + x^{3} + {179}x^{2} - {5}x - {2}} $\\ 913E& ${x^{17} - {9}x^{16} + {15}x^{15} + {91}x^{14} - {345}x^{13} - {66}x^{12} + {1859}x^{11} - {1804}x^{10} - {3615}x^{9} }$\\&${+ {6684}x^{8} + {1122}x^{7}- {8208}x^{6} + {3278}x^{5} + {2853}x^{4} - {2196}x^{3} + {358}x^{2} - {5}x - 1} $\\ 913F& ${x^{5} - x^{4} - {5}x^{3} + {3}x^{2} + {4}x - 1} $\\ 913G& ${x^{15} + {7}x^{14} + {2}x^{13} - {82}x^{12} - {129}x^{11} + {328}x^{10} + {746}x^{9} - {524}x^{8} - {1707}x^{7} }$\\&${+ {286}x^{6} + {1801}x^{5} + {86}x^{4} - {831}x^{3} - {151}x^{2} + {133}x + {37}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{923}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 923A& ${x^{16} + {4}x^{15} - {13}x^{14} - {64}x^{13} + {52}x^{12} + {391}x^{11} - {28}x^{10} - {1164}x^{9} - {289}x^{8} }$\\&${+ {1761}x^{7} + {715}x^{6} - {1247}x^{5} - {608}x^{4} + {309}x^{3} + {152}x^{2} - {14}x - {5}} $\\ 923B& ${x^{10} + x^{9} - {11}x^{8} - {11}x^{7} + {38}x^{6} + {35}x^{5} - {49}x^{4} - {39}x^{3} + {18}x^{2} + {11}x - 1} $\\ 923C& ${x^{18} - {3}x^{17} - {25}x^{16} + {77}x^{15} + {249}x^{14} - {798}x^{13} - {1256}x^{12} + {4310}x^{11} + {3296}x^{10} }$\\&${- {13052}x^{9} - {3694}x^{8} + {22151}x^{7} - {1086}x^{6} - {19675}x^{5} + {5971}x^{4} + {7226}x^{3} }$\\&${- {3768}x^{2} - {160}x + {240}} $\\ 923D& ${x^{26} - {3}x^{25} - {39}x^{24} + {119}x^{23} + {659}x^{22} - {2050}x^{21} - {6346}x^{20} + {20159}x^{19} + {38611}x^{18}}$\\&${ - {125213}x^{17} - {155933}x^{16} + {513936}x^{15} + {428618}x^{14} - {1418685}x^{13} - {809799}x^{12} + {2630864}x^{11} }$\\&${+ {1043228}x^{10} - {3216012}x^{9} - {878901}x^{8} + {2486222}x^{7} + {428867}x^{6} - {1126309}x^{5} - {77770}x^{4} }$\\&${+ {259800}x^{3} - {15120}x^{2} - {22928}x + {3840}} $\\ 923E& ${x} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{943}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 943A& ${x - 1} $\\ 943B& ${x^{16} + {7}x^{15} + x^{14} - {91}x^{13} - {144}x^{12} + {405}x^{11} + {995}x^{10} - {661}x^{9} - {2772}x^{8} + {23}x^{7} + {3671}x^{6} }$\\&${+ {938}x^{5} - {2288}x^{4} - {777}x^{3} + {593}x^{2} + {176}x - {41}} $\\ 943C& ${x^{19} - {6}x^{18} - {11}x^{17} + {122}x^{16} - {23}x^{15} - {1007}x^{14} + {851}x^{13} + {4351}x^{12} - {4949}x^{11}}$\\&${ - {10657}x^{10} + {13195}x^{9} + {15208}x^{8} - {17642}x^{7} - {12700}x^{6} + {11260}x^{5} + {5628}x^{4} }$\\&${- {2855}x^{3} - {898}x^{2} + {237}x + {39}} $\\ 943D& ${x^{24} - {9}x^{23} + x^{22} + {213}x^{21} - {462}x^{20} - {1885}x^{19} + {6877}x^{18} + {6549}x^{17} - {47095}x^{16} }$\\&${+ {6084}x^{15} + {179298}x^{14} - {127891}x^{13} - {393376}x^{12} + {452990}x^{11} + {471970}x^{10} - {789081}x^{9} }$\\&${- {237645}x^{8} + {733769}x^{7} - {52371}x^{6} - {341822}x^{5} + {101462}x^{4} + {59331}x^{3} - {28895}x^{2} + {1832}x + {171}} $\\ 943E& ${x^{13} + {6}x^{12} - {60}x^{10} - {78}x^{9} + {183}x^{8} + {370}x^{7} - {154}x^{6} - {601}x^{5} - {120}x^{4} }$\\&${+ {300}x^{3} + {157}x^{2} + {23}x + 1} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{949}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 949A& ${x^{2} - {3}x + 1} $\\ 949B& ${x^{2} + x - 1} $\\ 949C& ${x^{16} + x^{15} - {24}x^{14} - {20}x^{13} + {234}x^{12} + {157}x^{11} - {1191}x^{10} - {620}x^{9} + {3367}x^{8} + {1308}x^{7} - {5160}x^{6} }$\\&${- {1437}x^{5} + {3799}x^{4} + {732}x^{3} - {937}x^{2} - {133}x - 1} $\\ 949D& ${x^{16} + {3}x^{15} - {17}x^{14} - {53}x^{13} + {108}x^{12} + {355}x^{11} - {320}x^{10} - {1132}x^{9} + {440}x^{8} + {1756}x^{7} - {208}x^{6} }$\\&${- {1219}x^{5} - {68}x^{4} + {363}x^{3} + {62}x^{2} - {37}x - {9}} $\\ 949E& ${x^{19} - {4}x^{18} - {21}x^{17} + {96}x^{16} + {165}x^{15} - {937}x^{14} - {556}x^{13} + {4791}x^{12} + {393}x^{11} - {13804}x^{10} }$\\&${+ {2384}x^{9} + {22463}x^{8} - {6559}x^{7} - {19460}x^{6} + {6378}x^{5} + {7664}x^{4} - {2215}x^{3} - {898}x^{2} + {64}x - 1} $\\ 949F& ${x^{18} + {3}x^{17} - {22}x^{16} - {68}x^{15} + {193}x^{14} + {622}x^{13} - {872}x^{12} - {2985}x^{11} + {2168}x^{10} + {8148}x^{9} }$\\&${- {2902}x^{8} - {12815}x^{7} + {1818}x^{6} + {11232}x^{5} - {216}x^{4} - {4962}x^{3} - {201}x^{2} + {835}x + {37}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{979}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 979A& ${x - 1} $\\ 979B& ${x^{17} + {4}x^{16} - {16}x^{15} - {74}x^{14} + {95}x^{13} + {547}x^{12} - {241}x^{11} - {2054}x^{10} + {141}x^{9} + {4103}x^{8} + {489}x^{7} }$\\&${- {4118}x^{6} - {966}x^{5} + {1663}x^{4} + {596}x^{3} - {94}x^{2} - {43}x - 1} $\\ 979C& ${x^{11} + {2}x^{10} - {11}x^{9} - {22}x^{8} + {37}x^{7} + {79}x^{6} - {38}x^{5} - {105}x^{4} - {5}x^{3} + {35}x^{2} + {5}x - 1} $\\ 979D& ${x^{18} - {4}x^{17} - {19}x^{16} + {90}x^{15} + {124}x^{14} - {811}x^{13} - {225}x^{12} + {3743}x^{11} - {952}x^{10} }$\\&${- {9378}x^{9} + {5261}x^{8} + {12404}x^{7} - {9477}x^{6} - {7697}x^{5} + {7275}x^{4} + {1621}x^{3}}$\\&${ - {2164}x^{2} + {32}x + {160}} $\\ 979E& ${x^{25} - {4}x^{24} - {34}x^{23} + {150}x^{22} + {472}x^{21} - {2405}x^{20} - {3367}x^{19} + {21590}x^{18} + {12144}x^{17}}$\\&${ - {119518}x^{16} - {11478}x^{15} + {424322}x^{14} - {75545}x^{13} - {975398}x^{12} + {328509}x^{11} + {1432194}x^{10}}$\\&${ - {602131}x^{9} - {1290914}x^{8} + {586606}x^{7}+ {662736}x^{6} - {303037}x^{5} - {172209}x^{4} }$\\&${+ {73684}x^{3} + {18592}x^{2} - {6016}x - {672}} $\\ 979F& ${x} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{989}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{3}$\\\hline 989A& ${x - {3}} $\\ 989B& ${x^{4} + {2}x^{3} - {5}x^{2} - {6}x + {4}} $\\ 989C& ${x^{24} - {8}x^{23} - {20}x^{22} + {305}x^{21} - {125}x^{20} - {4784}x^{19} + {7159}x^{18} + {39563}x^{17} - {87958}x^{16} }$\\&${- {181345}x^{15} + {547998}x^{14} + {421434}x^{13} - {1945873}x^{12} - {223618}x^{11} + {3950948}x^{10} - {1046125}x^{9} }$\\&${- {4283043}x^{8} + {2176204}x^{7} + {2045523}x^{6} - {1457455}x^{5} - {159844}x^{4} }$\\&${+ {252973}x^{3} - {52506}x^{2} + {3196}x + {16}} $\\ 989D& ${x^{22} - {11}x^{21} + {17}x^{20} + {222}x^{19} - {851}x^{18} - {1163}x^{17} + {9774}x^{16} - {3541}x^{15} - {51223}x^{14} + {57070}x^{13} }$\\&${+ {140536}x^{12} - {235130}x^{11} - {202509}x^{10} + {485883}x^{9} + {128009}x^{8} - {554328}x^{7} + {9227}x^{6} + {345207}x^{5} }$\\&${- {50118}x^{4} - {106767}x^{3} + {19237}x^{2} + {12406}x - {1964}} $\\ 989E& ${x^{16} + {11}x^{15} + {31}x^{14} - {68}x^{13} - {468}x^{12} - {324}x^{11} + {1924}x^{10} + {3278}x^{9} - {2190}x^{8} }$\\&${- {7920}x^{7} - {1828}x^{6} + {6736}x^{5} + {4031}x^{4} - {1527}x^{3} - {1509}x^{2} - {138}x + {52}} $\\ 989F& ${x^{10} + {5}x^{9} - {5}x^{8} - {52}x^{7} - {23}x^{6} + {135}x^{5} + {53}x^{4} - {136}x^{3} + {11}x^{2} + {15}x + 1} $\\ \hline\end{tabular}\end{minipage} } \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{1003}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{3}$\\\hline 1003A& ${x - {3}} $\\ 1003B& ${x - 1} $\\ 1003C& ${x - {2}} $\\ 1003D& ${x^{3} - {2}x^{2} - {5}x + {2}} $\\ 1003E& ${x^{10} + {7}x^{9} + {8}x^{8} - {34}x^{7} - {56}x^{6} + {67}x^{5} + {94}x^{4} - {66}x^{3} - {39}x^{2} + {18}x - 1} $\\ 1003F& ${x^{22} - {7}x^{21} - {24}x^{20} + {260}x^{19} + {65}x^{18} - {3924}x^{17} + {3122}x^{16} + {31442}x^{15} }$\\&${- {41051}x^{14} - {147389}x^{13} + {232957}x^{12} + {425192}x^{11} - {712621}x^{10} - {787756}x^{9} + {1209743}x^{8}}$\\&${ + {971082}x^{7} - {1052280}x^{6} - {768268}x^{5} + {324016}x^{4} + {292480}x^{3} + {49984}x^{2}}$\\&${ + {1472}x - {128}} $\\ 1003G& ${x^{16} + {7}x^{15} - {8}x^{14} - {154}x^{13} - {157}x^{12} + {1228}x^{11} + {2482}x^{10} - {3944}x^{9} }$\\&${- {13179}x^{8} + {1539}x^{7} + {30581}x^{6} + {17216}x^{5} - {25563}x^{4} - {27478}x^{3} - {1953}x^{2} }$\\&${+ {4266}x + {540}} $\\ 1003H& ${x^{4} + {2}x^{3} - {5}x^{2} - {6}x + {4}} $\\ 1003I& ${x^{18} - x^{17} - {35}x^{16} + {29}x^{15} + {504}x^{14} - {331}x^{13} - {3862}x^{12} + {1901}x^{11}}$\\&${ + {16995}x^{10} - {5784}x^{9} - {43240}x^{8} + {8592}x^{7} + {60913}x^{6} - {3090}x^{5} - {42652}x^{4}}$\\&${ - {5572}x^{3} + {11672}x^{2} + {3760}x + {128}} $\\ 1003J& ${x} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{1007}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 1007A& ${x - {2}} $\\ 1007B& ${x^{12} + {3}x^{11} - {12}x^{10} - {38}x^{9} + {47}x^{8} + {164}x^{7} - {68}x^{6} - {286}x^{5} }$\\&${+ {37}x^{4} + {196}x^{3} - {9}x^{2} - {37}x + {7}} $\\ 1007C& ${x^{12} + {5}x^{11} - {2}x^{10} - {42}x^{9} - {31}x^{8} + {116}x^{7} + {124}x^{6} - {130}x^{5} }$\\&${- {151}x^{4} + {54}x^{3} + {55}x^{2} - {3}x - 1} $\\ 1007D& ${x^{28} - {3}x^{27} - {42}x^{26} + {128}x^{25} + {773}x^{24} - {2398}x^{23} - {8210}x^{22} + {25984}x^{21} }$\\&${+ {55795}x^{20} - {180640}x^{19} - {254355}x^{18} + {845427}x^{17} + {792781}x^{16} - {2721726}x^{15} }$\\&${- {1686216}x^{14} + {6057517}x^{13} + {2381593}x^{12} - {9243830}x^{11} - {2066032}x^{10} + {9460131}x^{9} }$\\&${+ {842962}x^{8} - {6228602}x^{7} + {139290}x^{6} + {2443827}x^{5} - {281692}x^{4} - {487131}x^{3} }$\\&${+ {89497}x^{2} + {31575}x - {5878}} $\\ 1007E& ${x^{26} - {6}x^{25} - {24}x^{24} + {204}x^{23} + {143}x^{22} - {2957}x^{21} + {1313}x^{20} + {23773}x^{19} }$\\&${- {25728}x^{18} - {115036}x^{17} + {181081}x^{16} + {336456}x^{15} - {713409}x^{14} - {543569}x^{13} }$\\&${+ {1698815}x^{12} + {280790}x^{11} - {2424843}x^{10} + {511527}x^{9} + {1923915}x^{8} - {940458}x^{7} }$\\&${- {679950}x^{6} + {547980}x^{5} + {10922}x^{4} - {95345}x^{3} + {27015}x^{2} - {2450}x + {33}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{1027}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{2}$\\\hline 1027A& ${x^{18} + {6}x^{17} - {8}x^{16} - {106}x^{15} - {57}x^{14} + {715}x^{13} + {859}x^{12} - {2323}x^{11}}$\\&${ - {3741}x^{10} + {3768}x^{9} + {7603}x^{8} - {2785}x^{7} - {7585}x^{6} + {510}x^{5} + {3292}x^{4} + {241}x^{3}}$\\&${ - {361}x^{2} - {32}x + {8}} $\\ 1027B& ${x^{17} + {10}x^{16} + {22}x^{15} - {90}x^{14} - {431}x^{13} - {29}x^{12} + {2401}x^{11} + {2695}x^{10} }$\\&${- {5361}x^{9} - {10562}x^{8} + {3217}x^{7} + {16039}x^{6} + {4113}x^{5} - {9336}x^{4} - {4872}x^{3} }$\\&${+ {1239}x^{2} + {959}x + {64}} $\\ 1027C& ${x^{22} - {8}x^{21} - {3}x^{20} + {176}x^{19} - {281}x^{18} - {1465}x^{17} + {3952}x^{16} + {5282}x^{15} }$\\&${- {23404}x^{14} - {3893}x^{13} + {72142}x^{12} - {27611}x^{11} - {118500}x^{10} + {81451}x^{9} }$\\&${+ {98907}x^{8} - {85881}x^{7} - {39195}x^{6} + {38199}x^{5} + {6767}x^{4} - {6456}x^{3} - {880}x^{2} + {384}x + {64}} $\\ 1027D& ${x^{21} - {9}x^{20} + {8}x^{19} + {152}x^{18} - {425}x^{17} - {792}x^{16} + {4160}x^{15} + {64}x^{14}}$\\&${ - {18654}x^{13} + {13873}x^{12} + {43575}x^{11} - {55324}x^{10} - {51008}x^{9} + {99433}x^{8} + {19464}x^{7}}$\\&${ - {91617}x^{6} + {14906}x^{5} + {40363}x^{4} - {15992}x^{3} - {5632}x^{2} + {4032}x - {576}} $\\ 1027E& ${x} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{1037}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{3}$\\\hline 1037A& ${x^{2} - {3}x + 1} $\\ 1037B& ${x^{18} + {15}x^{17} + {74}x^{16} + {32}x^{15} - {926}x^{14} - {2681}x^{13} + {1400}x^{12} }$\\&${+ {17484}x^{11} + {19234}x^{10} - {33596}x^{9} - {85376}x^{8} - {19066}x^{7} + {105512}x^{6} + {102553}x^{5} }$\\&${- {8083}x^{4} - {61166}x^{3} - {35970}x^{2} - {8416}x - {704}} $\\ 1037C& ${x^{16} + {12}x^{15} + {42}x^{14} - {35}x^{13} - {502}x^{12} - {615}x^{11} + {1771}x^{10} + {3959}x^{9} }$\\&${- {2292}x^{8} - {9624}x^{7} + {120}x^{6} + {11416}x^{5} + {1974}x^{4} - {6425}x^{3} - {1318}x^{2} }$\\&${+ {1236}x + {279}} $\\ 1037D& ${x^{23} - {10}x^{22} + x^{21} + {291}x^{20} - {681}x^{19} - {3174}x^{18} + {12221}x^{17} + {14285}x^{16}}$\\&${ - {99365}x^{15} - {1412}x^{14} + {443287}x^{13} - {234259}x^{12} - {1144878}x^{11} + {904603}x^{10} }$\\&${+ {1756306}x^{9} - {1468367}x^{8} - {1677167}x^{7} + {1055365}x^{6} + {1036867}x^{5} - {217298}x^{4} - {323651}x^{3} }$\\&${- {67998}x^{2} - {672}x + {416}} $\\ 1037E& ${x^{22} - {14}x^{21} + {53}x^{20} + {131}x^{19} - {1375}x^{18} + {1742}x^{17} + {9953}x^{16} }$\\&${- {29511}x^{15} - {17727}x^{14} + {156246}x^{13} - {89995}x^{12} - {367795}x^{11} + {465214}x^{10} + {342047}x^{9} }$\\&${- {794956}x^{8} + {43663}x^{7} + {542531}x^{6} - {226103}x^{5} - {91437}x^{4} + {64966}x^{3} }$\\&${- {6527}x^{2} - {1202}x + {146}} $\\ \hline\end{tabular}\end{minipage} \noindent\begin{minipage}{\textwidth} \vspace{.2in}\noindent{\large $\mathbf{1067}$}\\[.05in] \begin{tabular}{|l|l|}\hline Form&Factor of $T_{13}$\\\hline 1067A& ${x^{2} + {2}x - {17}} $\\ 1067B& ${x^{2} + {6}x + {7}} $\\ 1067C& ${x^{14} + {25}x^{13} + {211}x^{12} + {319}x^{11} - {5205}x^{10} - {26815}x^{9} + {6316}x^{8} }$\\&${+ {322481}x^{7} + {509743}x^{6} - {1144277}x^{5} - {3041934}x^{4} + {773584}x^{3} + {4970173}x^{2}}$\\&${ + {1136520}x - {1051945}} $\\ 1067D& ${x^{23} - {31}x^{22} + {323}x^{21} - {373}x^{20} - {17818}x^{19} + {122314}x^{18} + {23968}x^{17} }$\\&${- {3280979}x^{16} + {10485339}x^{15} + {21218891}x^{14} - {176189305}x^{13} + {155668558}x^{12} }$\\&${+ {988194140}x^{11} - {2112849646}x^{10} - {2047373230}x^{9} + {8552932523}x^{8} - {102049391}x^{7} }$\\&${- {16065070244}x^{6} + {5765616786}x^{5} + {13791034932}x^{4} - {6488157369}x^{3} - {3539208616}x^{2} }$\\&${+ {2153862224}x - {205611392}} $\\ 1067E& ${x^{15} + {23}x^{14} + {179}x^{13} + {213}x^{12} - {4773}x^{11} - {28337}x^{10} - {44114}x^{9} }$\\&${+ {124591}x^{8} + {578605}x^{7} + {653875}x^{6} - {372448}x^{5} - {1226400}x^{4} - {550665}x^{3} }$\\&${+ {154818}x^{2} + {53831}x + {3416}} $\\ 1067F& ${x^{25} - {39}x^{24} + {547}x^{23} - {2007}x^{22} - {28941}x^{21} + {340125}x^{20} }$\\&${- {618675}x^{19} - {9773072}x^{18} + {59314293}x^{17} + {20147003}x^{16} }$\\&${- {1190555831}x^{15} + {2833660753}x^{14} + {8271323665}x^{13} - {44669586321}x^{12} + {10591618031}x^{11} }$\\&${+ {268605910227}x^{10} - {398322683771}x^{9} - {599389230806}x^{8} + {1720189666248}x^{7} }$\\&${- {42102336229}x^{6} - {2561015519636}x^{5} + {1187441668674}x^{4}+ {1349674851756}x^{3}}$\\&${ - {789142890382}x^{2} - {121020476167}x + {5645501986}} $\\ \hline\end{tabular}\end{minipage} \end{document}